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Functional Analysis
Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.
Topological Vector Spaces
With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on v
Fourier and Wavelet Analysis
This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets. The books approach emphasizes the role of the "selector" functions, and is not embedded in the usual engineering context, which makes the material more accessible to a wider audience. While there are several publications on the various individual topics, none combine or even include all of the above.
Functional Analysis and Valuation Theory
This book presents functional analysis over arbitrary valued fields and investigates normed spaces and algebras over fields with valuation, with attention given to the case when the norm and the valuation are nonarchimedean. It considers vector spaces over fields with nonarchimedean valuation.
p-adic Functional Analysis
A presentation of results in p-adic Banach spaces, spaces over fields with an infinite rank valuation, Frechet (and locally convex) spaces with Schauder bases, function spaces, p-adic harmonic analysis, and related areas. It showcases research results in functional analysis over nonarchimedean valued complete fields. It explores spaces of continuous functions, isometries, Banach Hopf algebras, summability methods, fractional differentiation over local fields, and adelic formulas for gamma- and beta-functions in algebraic number theory.
Advanced Courses of Mathematical Analysis III
This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of the present-day research in different areas of mathematical analysis (complex variable, harmonic analysis, real analysis and functional analysis) that holds great promise for current and future developments. These review articles are highly useful for those who want to learn about these topics, as many results scattered in the literature are reflected through the many separate papers featured herein.
Elements of Abstract Harmonic Analysis
Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give a brief review of classical Fourier analysis and present concepts which will subsequently be generalized to a more abstract framework. The next five chapters present an introduction to commutative Banach algebras, general topological spaces, and topological groups. The remaining chapters contain some of the measure theoretic background, including the Haar integral, and an extension of the concepts of the first two chapters to Fourier analysis on locally compact topological abelian groups.
Advanced Courses of Mathematical Analysis II
This volume comprises a collection of articles by leading researchers in mathematical analysis. It provides the reader with an extensive overview of new directions and advances in topics for current and future research in the field. Contents: Lineable and Spaceable Properties (R M Aron); Alexander Grothendieck's Work on Functional Analysis (F Bombal); Maximal Functions in Fourier Analysis (J Duoandikoetxea); Hypercyclic Operators: Some Recent Progress (G Godefroy); On the Hahn-Banach Theorem (L Narici); Lipschitz Quotient Maps Between Banach Spaces (W B Johnson); Approximation Algorithms in Banach Spaces (N Kalton); Spectral Properties of Cesa'ro-Like Operators (M M Neumann); Some Ideas on Mathematical Training Concerning Mathematical Analysis (B Rubio); Interpolation and Sampling (K Seip); Classes of Indefinitely Differentiable Functions (M Valdivia); Classical Potential Theory and Analytic Capacity (J Verdera); Best Approximations on Small Regions: A General Approach (F Zo & H H Cuenya). Readership: Mathematicians in analysis and differential equations and approximation theory.
