Continuity, integration and Fourier theory
type: Item
instance of: scholarly article
title: Continuity, integration and Fourier theory
zbMATH Open document ID: 0671.42001
author: Adriaan C. Zaanen
published in: Universitext
publication date: 1992-09-17T00:00:00Z
review text: This book is a textbook for graduate or advanced undergraduate students in mathematics and mathematical physics. It is devided in eight chapters: 1. The space of continuous functions. 2. Theorems of Korovkin and Stone- Weierstrass, 3. Fourier series of continuous functions, 4. Integration and differentiation, 5. Spaces \(L_ p\) and convolutions, 6. Fourier series of summable functions, 7. Fourier integral, 8. Additional results. The first two chapters are devoted to real or complex continuous functions on \({\mathbb{R}}^ k\) and the third to the elementary theory of Fourier series. Chapters 4 and 5 deal with integration theory of Lebesgue measure in Euclidean space as well as for abstract measures. The presentation is brief but with complete proofs. The topics of chapters 6 and 7 are the Riesz-Fisher theorem and the Plancherel theorem, respectively. The last chapter is concerned with various applications, for instance: Functions of analytic type, the Hausdorff-Young theorem, the Heat equation. The book contains more than 60 adequate exercises and ends with a list of references and subject index.
reviewed by: S.Aljančić
Mathematics Subject Classification ID: 42-01
Mathematics Subject Classification ID: 26-01
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A36
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 42A20
zbMATH DE Number: 42074
zbMATH Keywords: Korovkin
zbMATH Keywords: Stone-Weierstrass
zbMATH Keywords: Fourier series of continuous functions
zbMATH Keywords: convolutions
zbMATH Keywords: Lebesgue measure
zbMATH Keywords: Riesz-Fisher theorem
zbMATH Keywords: Plancherel theorem
zbMATH Keywords: Hausdorff-Young theorem
zbMATH Keywords: Heat equation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 42074