Continuity, Integration and Fourier Theory

Continuity, Integration and Fourier Theory

Author: Adriaan C. Zaanen

Publisher: Springer Science & Business Media

ISBN: 9783642738852

Category: Mathematics

Page: 251

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This book is a textbook for graduate or advanced undergraduate students in mathematics and (or) mathematical physics. It is not primarily aimed, therefore, at specialists (or those who wish to become specialists) in integra tion theory, Fourier theory and harmonic analysis, although even for these there might be some points of interest in the book (such as for example the simple remarks in Section 15). At many universities the students do not yet get acquainted with Lebesgue integration in their first and second year (or sometimes only with the first principles of integration on the real line ). The Lebesgue integral, however, is indispensable for obtaining a familiarity with Fourier series and Fourier transforms on a higher level; more so than by us ing only the Riemann integral. Therefore, we have included a discussion of integration theory - brief but with complete proofs - for Lebesgue measure in Euclidean space as well as for abstract measures. We give some emphasis to subjects of which an understanding is necessary for the Fourier theory in the later chapters. In view of the emphasis in modern mathematics curric ula on abstract subjects (algebraic geometry, algebraic topology, algebraic number theory) on the one hand and computer science on the other, it may be useful to have a textbook available (not too elementary and not too spe cialized) on the subjects - classical but still important to-day - which are mentioned in the title of this book.
Continuity, Integration and Fourier Theory
Language: en
Pages: 251
Authors: Adriaan C. Zaanen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

This book is a textbook for graduate or advanced undergraduate students in mathematics and (or) mathematical physics. It is not primarily aimed, therefore, at specialists (or those who wish to become specialists) in integra tion theory, Fourier theory and harmonic analysis, although even for these there might be some points
Operator Theory in Function Spaces and Banach Lattices
Language: en
Pages: 309
Authors: C.B. Huijsmans, M.A. Kaashoek, W.A.J. Luxemburg, B.de Pagter
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains
Real Analysis
Language: en
Pages: 401
Authors: N. L. Carothers
Categories: Mathematics
Type: BOOK - Published: 2000-08-15 - Publisher: Cambridge University Press

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Theory and Numerics of Differential Equations
Language: en
Pages: 282
Authors: James Blowey, John P. Coleman, Alan W. Craig
Categories: Mathematics
Type: BOOK - Published: 2001-08-28 - Publisher: Springer Science & Business Media

A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the
Riemannian Geometry and Geometric Analysis
Language: en
Pages: 458
Authors: Jürgen Jost
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Springer Science & Business Media

FROM REVIEWS OF THE FIRST EDITION "a very readable introduction to Riemannian geometry...it is most welcome...The book is made more interesting by the perspectives in various sections, where the author mentions the history and development of the material and provides the reader with references."-MATHEMATICAL REVIEWS