Albrecht Pietsch – författare
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13 produkter
13 produkter
Del 70 - Encyclopedia of Mathematics and its Applications
Orthonormal Systems and Banach Space Geometry
Häftad, Engelska, 2008
747 kr
Skickas inom 7-10 vardagar
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.
Del 70 - Encyclopedia of Mathematics and its Applications
Orthonormal Systems and Banach Space Geometry
Inbunden, Engelska, 1998
2 252 kr
Skickas inom 7-10 vardagar
Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.
Inbunden, Engelska, 2007
2 495 kr
Skickas inom 10-15 vardagar
Named for one of the great mathematicians of the twentieth century, Banach spaces figure prominently in the study of functional analysis, having applications to integral and differential equations, approximation theory, harmonic analysis, convex geometry, numerical mathematics, analytic complexity, and probability theory. This work, written by a distinguished specialist in functional analysis, is devoted to a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. While other comprehensive texts on Banach spaces focus on developments before 1950, this one is mainly devoted to the second half of the twentieth century. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. Numerous examples and counterexamples elucidate the scope of the underlying concepts. As a stimulus for further research, the text also contains many problems which have not been previously solved.The book may serve as a reference and introduction for graduate students and researchers who want to learn Banach space theory with some historical flavor.
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PDF, Engelska, 20073 046 kr
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make it look much more logical, but actually it happens quite differently. • Atiyah [2004 ] The monographs A. F. Monna: Functional Analysis in Historical Perspective (1973), and J. Dieudonne: ´ History of Functional Analysis (1981), as well as all articles devoted to the history of functional analysis deal only with the development before 1950. Now the time has come to cover the second half of the twentieth century too. I have undertaken this adventure. Let me introduce myself by telling you that I received my M. Sc. degree in 1958, just at the time when the renaissance of Banach space theory started. Thus I have ?rst-hand experience of the progress achieved during the past 50 years. Due to the explosion of knowledge, writing about functional analysis as a whole seems to be no longer possible. Hence this book is focused on Banach spaces and (abstract bounded) linear operators. Other subjects such as topologies, measures and integrals, locally convex linear spaces, Banach lattices, and Banach algebras are treated only in so far as they turn out to be relevant for this purpose. The interplay with set theory is described carefully: Which axioms are needed in order to prove the Hahn–Banach theorem? Results about non-self-adjoint operators on Hilbert spaces have been a source of inspiration for the theory of operators on Banach spaces. Such topics are discussed in great detail. However, I have omitted almost all operator-theoretic considerations that depend decisively on the existence of an inner product.
Inbunden, Engelska, 1973
1 773 kr
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No detailed description available for "Nuclear Locally Convex Spaces".
E-bok
PDF, Engelska, 20221 410 kr
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No detailed description available for "e;Nuclear Locally Convex Spaces"e;.
Del 12 - Schriftenreihe der Institute Für Mathematik Bei der Deutschen Akademie der Wissenschaften Zu Berlin/
Verallgemeinerte Vollkommene Folgenräume
Inbunden, Tyska, 1962
2 206 kr
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E-bok
PDF, Tyska, 19621 650 kr
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Keine ausführliche Beschreibung für "Verallgemeinerte vollkommene Folgenräume" verfügbar.
Del 1 - Schriftenreihe der Institute Für Mathematik Bei der Deutschen Akademie der Wissenschaften Zu Berlin/
Nukleare Lokalkonvexe Räume
Inbunden, Tyska, 1969
2 200 kr
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E-bok
PDF, Tyska, 19691 650 kr
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Keine ausführliche Beschreibung für "Nukleare lokalkonvexe Räume" verfügbar.
Häftad, Tyska, 1989
513 kr
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E-bok
PDF, Tyska, 2014471 kr
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Häftad, Engelska, 2012
548 kr
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VI closely related to finite dimensional locally convex spaces than are normed spaces. In order to present a clear narrative I have omitted exact references to the literature for individual propositions. However, each chapter begins with a short introduction which also contains historical remarks. Deutsche Akademie der vVissenschaften zu Berlin Institut fur Reine Mathematik Albrecht Pietsch Foreword to the Second Edition Since the appearance of the first edition, some important advances have taken place in the theory of nuclear locally convex spaces. Firsts there is the Universality Theorem ofT. and Y. Komura which fully confirms a conjecture of Grothendieck. Also, of particular interest are some new existence theorems for bases in special nuclear locally convex spaces. Recently many authors have dealt with nuclear spaces of functions and distributions. Moreover, further classes of operators have been found which take the place of nuclear or absolutely summing operators in the theory of nuclear locally convex spaces. Unfortunately, there seem to be no new results on diametrai or approximative dimension and isomorphism of nuclear locally convex spaces. Since major changes have not been absolutely necessary I have restricted myself to minor additions. Only the tenth chapter has been substantially altered. Since the universality results no longer depend on the existence of a basis it was necessary to introduce an independent eleventh chapter on universal nuclear locally convex spaces. In the same chapter s-nuclear locally convex spaces are also briefly treated.