Theory of Function Spaces

Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Holder

This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the th

The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional ana

Kosmol (Christian-Albrechts-U.,Kiel) and Muller-Wichards (information and electronics, Hamburg U. of Applied Sciences) present a concise but thorough account of convex analysis as a foundation for tre

This monograph is devoted to the study of Kothe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A n

From the reviews: "... the book is written in the best tradition of the beautiful series in which it appears. The material it presents is hard to find in other books. For people working in the structu

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has compl

Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introductio

This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These incl

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

This volume collects a selected number of papers presented at the International Workshop on Operator Theory and its Applications (IWOTA) held in July 2014 at Vrije Universiteit in Amsterdam. Main deve

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in t

Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form ½+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line ½+it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of ζ(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research.

The fundamental contributions of Professor Maz'ya to the theory of function spaces and especially Sobolev spaces are well known and often play a key role in the study of different aspects of the theor

A complete and self-contained account of the dimension theory of general topological spaces, with particular emphasis on the dimensional properties of non-metrizable spaces. It makes the subject accessible to beginning graduate students and will also serve as a reference work for general topologists. Two introductory chapters summarize standard results in general topology, and cover material on paracompactness and metrization. The principal definitions of dimension follow and their general properties are deduced. Many examples are analysed to show some of the more surprising or pathological aspects of dimension theory. Wherever it is useful to do so, proofs are given in detail.

Advances a permanent-income hypothesis concerning consumption expenditure and income, proceeding from the pure theory of consumer behavior, incorporating the wealth-income effect, and explaining the v

The distribution of the eigenvalues of differential operators has long fascinated mathematicians. Advances have shed light upon classical problems in this area, and this book presents a fresh approach, largely based upon the results of the authors. The emphasis here is on a topic of central importance in analysis, namely the relationship between i) function spaces on Euclidean n-space and on domains; ii) entropy numbers in quasi-Banach spaces; and iii) the distribution of the eigenvalues of degenerate elliptic (pseudo) differential operators. The treatment is largely self-contained and accessible to non-specialists. Both experts and newcomers alike will welcome this unique exposition.

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in t

This book is about harmonic functions in Euclidean space. This new edition contains a completely rewritten chapter on spherical harmonics, a new section on extensions of Bochers Theorem, new exercises

Winner of the Intro Prize