CBMS Regional Conference Series in Mathematics – serie
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85 produkter
85 produkter
461 kr
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Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher - one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.
368 kr
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This CBMS lecture series, held in Albany, New York in June 1994, aimed to introduce the audience to the literature on complex dynamics in higher dimension. Some of the lectures are updated versions of earlier lectures given jointly with Nessim Sibony in Montreal 1993. The author's intent in this book is to give an expansion of the Montreal lectures, basing complex dynamics in higher dimension systematically on pluripotential theory. These notes provide an easy-to-read introduction into the field, an introduction that motivates the topics. The monograph then points readers towards technically more advanced literature.
727 kr
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This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology.Finally, the book gives an introduction to 'brave new algebra', the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail. It introduces many of the fundamental ideas and concepts of modern algebraic topology. It presents comprehensive material not found in any other book on the subject. It provides a coherent overview of many areas of current interest in algebraic topology. It surveys a great deal of material, explaining main ideas without getting bogged down in details.
340 kr
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Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin $1/2$ XXZ chain and the six-vertex model.The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the $XXX$ model is briefly discussed, and the book closes with a discussion of other types of models and related works.
340 kr
Skickas
This monograph provides a more unified and self-contained presentation of the results presented in Popa's earlier papers on this topic. The classification is in terms of the standard invariant $\mathcal G_{\mathcal N,\mathcal M} $ of the subfactor $\mathcal N\subset \mathcal M$. This invariant is a lattice of inclusions of finite dimensional algebras associated with the Jones iterated basic construction for $\mathcal N\subset \mathcal M$. ""Classification of Subfactors and Their Endomorphisms"" is based on lectures presented by Popa at the NSF-CBMS Regional Conference held in Eugene, Oregon, in August 1993.
368 kr
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This book presents the expanded notes from ten lectures given by the author at the NSF/CBMS conference held at California State University (Bakersfield). The author describes what he calls single orbit dynamics, which is an approach to the analysis of dynamical systems via the study of single orbits, rather than the study of a system as a whole. He presents single orbit interpretations of several areas of topological dynamics and ergodic theory and some new applications of dynamics to graph theory. In the concluding lectures, single orbit approaches to generalizations of the Shannon-Breiman-McMillan theorem and related problems of compression and universal coding are presented. Complete proofs and illuminating discussions are included and references for further study are given. Some of the material appears here for the first time in print.
407 kr
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The first part of the book is devoted to an account of various aspects of the theory of harmonic maps between Riemannian manifolds. The second part proposes certain unsolved problems, together with comments and references, which are of widely varying difficulty. This book presents the first printed exposition of the qualitative aspects of harmonic maps.
382 kr
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This book contains expository lectures from the CBMS Regional Conference held at the University of Florida, 1982. The author considers a space formed by all closed curves in which the closed geodesics are characterized as the critical points of a functional, an idea going back to Morse. This exposition gives a refined version of Morse's approach which has several advantages over the old one - in particular, it possesses a canonical $\mathbf O(2)$-action.
394 kr
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This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSF-supported CBMS conference at George Mason University, held June 27-July 1, 1983.The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the self-intersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; and Riemann-Roch theorems.
399 kr
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This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.
368 kr
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These notes were the basis for a series of ten lectures given in January 1984 at Polytechnic Institute of New York under the sponsorship of the Conference Board of the Mathematical Sciences and the National Science Foundation. The lectures were aimed at mathematicians who knew either some differential geometry or partial differential equations, although others could understand the lectures. Author's Summary: Given a Riemannian Manifold $(M,g)$ one can compute the sectional, Ricci, and scalar curvatures. In other special circumstances one also has mean curvatures, holomorphic curvatures, etc.The inverse problem is, given a candidate for some curvature, to determine if there is some metric $g$ with that as its curvature. One may also restrict ones attention to a special class of metrics, such as Kahler or conformal metrics, or those coming from an embedding. These problems lead one to (try to) solve nonlinear partial differential equations. However, there may be topological or analytic obstructions to solving these equations. A discussion of these problems thus requires a balanced understanding between various existence and non-existence results. The intent of this volume is to give an up-to-date survey of these questions, including enough background, so that the current research literature is accessible to mathematicians who are not necessarily experts in PDE or differential geometry. The intended audience is mathematicians and graduate students who know either PDE or differential geometry at roughly the level of an intermediate graduate course.
340 kr
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This book introduces a systematic new approach to the construction and analysis of semi simple $p$-adic groups. The basic construction presented here provides an analogue in certain cases of the Harish-Chandra homomorphism, which has played an essential role in the theory of semi simple Lie groups. The book begins with an overview of the representation theory of GL$_n$ over finite groups.The author then explicitly establishes isomorphisms between certain convolution algebras of functions on two different groups. Because of the form of the isomorphisms, basic properties of representations are preserved, thus giving a concrete example to the correspondences predicted by the general philosphy of Langlands. The first chapter, suitable as an introduction for graduate students, requires only a basic knowledge of representation theory of finite groups and some familiarity with the general linear group and the symmetric group. The later chapters introduce researchers in the field to a new method for the explicit construction and analysis of representations of $p$-adic groups, a powerful method clearly capable of extensive further development.
407 kr
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This book surveys the considerable progress made in Banach space theory as a result of Grothendieck's fundamental paper ""Resume De la Theorie Metrique des Produits Tensoriels Topologiques"". The author examines the central question of which Banach spaces $X$ and $Y$ have the property that every bounded operator from $X$ to $Y$ factors through a Hilbert space, in particular when the operators are defined on a Banach lattice, a $C^*$-algebra or the disc algebra and $H^\infty$. He reviews the six problems posed at the end of Grothendieck's paper, which have now all been solved (except perhaps the exact value of Grothendieck's constant), and includes the various results which led to their solution. The last chapter contains the author's construction of several Banach spaces such that the injective and projective tensor products coincide; this gives a negative solution to Grothendieck's sixth problem.Although the book is aimed at mathematicians working in functional analysis, harmonic analysis and operator algebras, its detailed and self-contained treatment makes the material accessible to nonspecialists with a grounding in basic functional analysis. In fact, the author is particularly concerned to develop very recent results in the geometry of Banach spaces in a form that emphasizes how they may be applied in other fields, such as harmonic analysis and $C^*$-algebras.
368 kr
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Harmonic analysis on Riemannian semi simple symmetric spaces and on special types of non-Riemannian semi simple symmetric spaces are well-established theories. This book presents a systematic treatment of the basic problems on semi simple symmetric spaces and a discussion of some of the more important recent developments in the field. The author's primary contribution has been his idea of how to construct the discrete series for such a space.In this book a fundamental role is played by the ideas behind that construction, namely the duality principle, the orbit picture related to it, and the definition of representations by means of distributions on the orbits. Intended as a text at the upper graduate level, the book assumes a basic knowledge of Fourier analysis, differential geometry, and functional analysis. In particular, the reader should have a good knowledge of the general theory of real and complex Lie algebras and Lie groups and of the root and weight theories for semi simple Lie algebras and Lie groups.
Extremal Graph Theory with Emphasis on Probabilistic Methods Expository Lectures
Regional Conference
Häftad, Engelska, 1986
365 kr
Skickas inom 11-20 vardagar
Problems in extremal graph theory have traditionally been tackled by ingenious methods which made use of the structure of extremal graphs. In this book, an update of his 1978 book ""Extremal Graph Theory"", the author focuses on a trend towards probabilistic methods. He demonstrates both the direct use of probability theory and, more importantly, the fruitful adoption of a probabilistic frame of mind when tackling main line extremal problems. Essentially self-contained, the book does not merely catalog results, but rather includes considerable discussion on a few of the deeper results. The author addresses pure mathematicians, especially combinatorialists and graduate students taking graph theory, as well as theoretical computer scientists. He assumes a mature familiarity with combinatorial methods and an acquaintance with basic graph theory. The book is based on the NSF-CBMS Regional Conference on Graph Theory held at Emory University in June, 1984.
New Constructions of Functions Holomorphic in the Unit Ball of CN Expository Lectures
Regional Conference
Häftad, Engelska, 1986
421 kr
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The starting point for the research presented in this book is A. B. Aleksandrov's proof that nonconstant inner functions exist in the unit ball $B$ of $C^n$. The construction of such functions has been simplified by using certain homogeneous polynomials discovered by Ryll and Wojtaszczyk; this yields solutions to a large number of problems. The lectures, presented at a CBMS Regional Conference held in 1985, are organized into a body of results discovered in the preceding four years in this field, simplifying some of the proofs and generalizing some results. The book also contains results that were obtained by Monique Hakina, Nessim Sibony, Erik Low and Paula Russo. Some of these are new even in one variable. An appreciation of techniques not previously used in the context of several complex variables will reward the reader who is reasonably familiar with holomorphic functions of one complex variable and with some functional analysis.
Minimax Methods in Critical Point Theory with Applications to Differential Equations Lectures
Regional Conference
Häftad, Engelska, 1986
365 kr
Skickas inom 11-20 vardagar
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
Q - Series
Their Development and Application in an Analysis, Number Theory, Combinatorics, Physics and Computer Algebra
Häftad, Engelska, 1986
327 kr
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This book integrates recent developments and related applications in $q$-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's ""Lost Notebook."" With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra. It is understandable to even a beginning graduate student in mathematics who has a background in advanced calculus and some mathematical maturity.
Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics
Regional Conference
Häftad, Engelska, 1987
354 kr
Skickas inom 11-20 vardagar
This book is based on the CBMS Regional Conference held at the University of California, Irvine, in July 1985. Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. The author describes some relevant results and puts them in a general framework, based on the concepts of $JB$-algebra and $JB^\ast$-triple.
436 kr
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This book expands the lectures given at a regional conference in Lincoln, Nebraska which brought together a wide variety of scientists, pure mathematicians and engineers.
356 kr
Skickas inom 11-20 vardagar
$J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation
Häftad, Engelska, 1989
440 kr
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This book evolved from a set of lectures presented under the auspices of the Conference Board of Mathematical Sciences at the Case Institute of Technology in September 1984. The original objective of the lectures was to present an introduction to the theory and applications of $J$ inner matrices. However, in revising the lecture notes for publication, the author began to realize that the spaces ${\mathcal H}(U)$ and ${\mathcal H}(S)$ are ideal tools for treating a large class of matrix interpolation problems including ultimately two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these. Consequently, the lecture notes were revised to bring ${\mathcal H}(U)$ and ${\mathcal H}(S)$ to center stage. This monograph is the first systematic exposition of the use of these spaces for interpolation problems.
274 kr
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The author surveys a wide collection of techniques for showing the existence of solutions to various nonlinear partial differential equations, especially when strong analytic estimates are unavailable. The overall guiding viewpoint is that when a sequence of approximate solutions converges only weakly, one must exploit the nonlinear structure of the PDE to justify passing to limits. The author concentrates on several areas that are rapidly developing and points to some underlying viewpoints common to them all. Among the several themes in the book are the primary role of measure theory and real analysis (as opposed to functional analysis) and the continual use in diverse settings of low-amplitude, high-frequency periodic test functions to extract useful information. The author uses the simplest problems possible to illustrate various key techniques. Aimed at research mathematicians in the field of nonlinear PDEs, this book should prove an important resource for understanding the techniques being used in this important area of research.
365 kr
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The theory of nonlinear wave equations in the absence of shocks began in the 1960s. Despite a great deal of recent activity in this area, some major issues remain unsolved, such as sharp conditions for the global existence of solutions with arbitrary initial data, and the global phase portrait in the presence of periodic solutions and traveling waves. This book, based on lectures presented by the author at George Mason University in January 1989, seeks to present the sharpest results to date in this area.The author surveys the fundamental qualitative properties of the solutions of nonlinear wave equations in the absence of boundaries and shocks. These properties include the existence and regularity of global solutions, strong and weak singularities, asymptotic properties, scattering theory and stability of solitary waves. Wave equations of hyperbolic, Schrodinger, and KdV type are discussed, as well as the Yang-Mills and the Vlasov-Maxwell equations. The book offers readers a broad overview of the field and an understanding of the most recent developments, as well as the status of some important unsolved problems. Intended for mathematicians and physicists interested in nonlinear waves, this book would be suitable as the basis for an advanced graduate-level course.
554 kr
Skickas inom 5-8 vardagar
411 kr
Skickas inom 11-20 vardagar
Littlewood Paley Theory and the Study of Functional Spaces Papers
Regional Conference
Häftad, Engelska, 1991
647 kr
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Littlewood-Paley theory was developed to study function spaces in harmonic analysis and partial differential equations. Recently, it has contributed to the development of the $\varphi$-transform and wavelet decompositions. Based on lectures presented at the NSF-CBMS Regional Research Conference on Harmonic Analysis and Function Spaces, held at Auburn University in July 1989, this book is aimed at mathematicians, as well as mathematically literate scientists and engineers interested in harmonic analysis or wavelets. The authors provide not only a general understanding of the area of harmonic analysis relating to Littlewood-Paley theory and atomic and wavelet decompositions, but also some motivation and background helpful in understanding the recent theory of wavelets.The book begins with some simple examples which provide an overview of the classical Littlewood-Paley theory. The $\varphi$-transform, wavelet, and smooth atomic expansions are presented as natural extensions of the classical theory. Finally, applications to harmonic analysis (Calderon-Zygmund operators), signal processing (compression), and mathematical physics (potential theory) are discussed.
428 kr
Skickas inom 11-20 vardagar
This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. This book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.
Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis
Häftad, Engelska, 1994
514 kr
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This book contains lectures presented by Hugh L. Montgomery at the NSF-CBMS Regional Conference held at Kansas State University in May 1990. The book focuses on important topics in analytic number theory that involve ideas from harmonic analysis. One valuable aspect of the book is that it collects material that was either unpublished or that had appeared only in the research literature. This book would be an excellent resource for harmonic analysts interested in moving into research in analytic number theory. In addition, it is suitable as a textbook in an advanced graduate topics course in number theory.
508 kr
Skickas inom 11-20 vardagar
The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves.The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups.