N.K. Nikol'skij – författare
Visar alla böcker från författaren N.K. Nikol'skij. Handla med fri frakt och snabb leverans.
5 produkter
5 produkter
Del 15 - Encyclopaedia of Mathematical Sciences
Commutative Harmonic Analysis I
General Survey. Classical Aspects
Inbunden, Engelska, 1991
1 073 kr
Skickas inom 10-15 vardagar
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer- rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "mini-Zygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail.There is also a thorough introduction to Calderon-Zygmund theory.
Del 19 - Encyclopaedia of Mathematical Sciences
Functional Analysis I
Linear Functional Analysis
Inbunden, Engelska, 1992
1 286 kr
Skickas inom 10-15 vardagar
The twentieth century view of the analysis of functions is dominated by the study of classes of functions, as contrasted with the older emphasis on the study of individual functions. Operator theory has had a similar evolution, leading to a primary role for families of operators. This volume of the Encyclopaedia covers the origins, development and applications of linear functional analysis, explaining along the way how one is led naturally to the modern approach. The book consists of two chapters, the first of which deals with classical aspects of the subject, while the second presents the abstract modern theory and some of its applications. Both chapters are divided into sections which are devoted to individual topics. For each topic the origins are traced, the principal definitions and results are stated and illustrative examples for theory and applications are given. Usually proofs are omitted, although certain sections of Chapter 2 do contain some quite detailed proofs. The classical concrete problems of Chapter 1 provide motivation and examples, as well as a technical foundation, for the theory in Chapter 2.
Häftad, Engelska, 2010
1 073 kr
Skickas inom 10-15 vardagar
This is the first volume in the subseries Commutative Harmonic Analysis of the EMS. It is intended for anyone who wants to get acquainted with the discipline. The first article is a large introduction, also serving as a guide to the rest of the volume. Starting from Fourier analysis of periodic function, then going through the Fourier transform and distributions, the exposition leads the reader to the group theoretic point of view. Numer- rous examples illustrate the connections to differential and integral equations, approximation theory, number theory, probability theory and physics. The article also contains a brief historical essay on the development of Fourier analysis. The second article focuses on some of the classical problems of Fourier series; it's a "mini-Zygmund" for the beginner. In particular, the convergence and summability of Fourier series, translation invariant operators and theorems on Fourier coefficients are given special attention. The third article is the most modern of the three, concentrating on the theory of singular integral operators. The simplest such operator, the Hilbert transform, is covered in detail.There is also a thorough introduction to Calderon-Zygmund theory.
Del 19 - Encyclopaedia of Mathematical Sciences
Functional Analysis I
Linear Functional Analysis
Häftad, Engelska, 2010
1 286 kr
Skickas inom 10-15 vardagar
Up to a certain time the attention of mathematicians was concentrated on the study of individual objects, for example, specific elementary functions or curves defined by special equations. With the creation of the method of Fourier series, which allowed mathematicians to work with 'arbitrary' functions, the individual approach was replaced by the 'class' approach, in which a particular function is considered only as an element of some 'function space'. More or less simultane ously the development of geometry and algebra led to the general concept of a linear space, while in analysis the basic forms of convergence for series of functions were identified: uniform, mean square, pointwise and so on. It turns out, moreover, that a specific type of convergence is associated with each linear function space, for example, uniform convergence in the case of the space of continuous functions on a closed interval. It was only comparatively recently that in this connection the general idea of a linear topological space (L TS)l was formed; here the algebraic structure is compatible with the topological structure in the sense that the basic operations (addition and multiplication by a scalar) are continuous.
Del 72 - Encyclopaedia of Mathematical Sciences
Commutative Harmonic Analysis III
Generalized Functions. Application
Häftad, Engelska, 2012
540 kr
Skickas inom 10-15 vardagar
The theory of generalized functions is a general method that makes it possible to consider and compute divergent integrals, sum divergent series, differentiate discontinuous functions, perform the operation of integration to any complex power and carry out other such operations that are impossible in classical analysis. Such operations are widely used in mathematical physics and the theory of differential equations, where the ideas of generalized func tions first arose, in other areas of analysis and beyond. The point of departure for this theory is to regard a function not as a mapping of point sets, but as a linear functional defined on smooth densi ties. This route leads to the loss of the concept of the value of function at a point, and also the possibility of multiplying functions, but it makes it pos sible to perform differentiation an unlimited number of times. The space of generalized functions of finite order is the minimal extension of the space of continuous functions in which coordinate differentiations are defined every where. In this sense the theory of generalized functions is a development of all of classical analysis, in particular harmonic analysis, and is to some extent the perfection of it. The more general theories of ultradistributions or gener alized functions of infinite order make it possible to consider infinite series of generalized derivatives of continuous functions.