
Harmonic Analysis
American Mathematical Society (Publisher)
Published on 30. May 2022
Book
Paperback/Softback
105 pages
978-1-4704-6507-0 (ISBN)
Description
Harmonic Analysis is an important tool that plays a vital role in many areas of mathematics as well as applications. It studies functions by decomposing them into components that are special functions. A prime example is decomposing a periodic function into a linear combination of sines and cosines. The subject is vast, and this book covers only the selection of topics that was dealt with in the course given at the Courant Institute in 2000 and 2019. These include standard topics like Fourier series and Fourier transforms of functions, as well as issues of convergence of Abel, Feier, and Poisson sums. At a slightly more advanced level the book studies convolutions with singular integrals, fractional derivatives, Sobolev spaces, embedding theorems, Hardy spaces, and BMO. Applications to elliptic partial differential equations and prediction theory are explored. Some space is devoted to harmonic analysis on compact non-Abelian groups and their representations, including some details about two groups: the permutation group and SO(3).
The text contains exercises at the end of most chapters and is suitable for advanced undergraduate students as well as first- or second-year graduate students specializing in the areas of analysis, PDE, probability or applied mathematics.
The text contains exercises at the end of most chapters and is suitable for advanced undergraduate students as well as first- or second-year graduate students specializing in the areas of analysis, PDE, probability or applied mathematics.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
216 gr
ISBN-13
978-1-4704-6507-0 (9781470465070)
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Schweitzer Classification
Persons
S.R.S. Varadhan, Courant Institute, New York University, NY.
Content
Fourier Series
Fourier Transforms on $\mathbb{R}^d$
Singular Integrals
Riesz Transforms on $\mathbb{R}^d$
Sobolev Spaces
Hardy Spaces
Bounded Mean Oscillation
Elliptic PDEs
Banach Algebras and Wiener's Theorem
Compact Groups
Representations of Two Compact Groups
References
Index
Fourier Transforms on $\mathbb{R}^d$
Singular Integrals
Riesz Transforms on $\mathbb{R}^d$
Sobolev Spaces
Hardy Spaces
Bounded Mean Oscillation
Elliptic PDEs
Banach Algebras and Wiener's Theorem
Compact Groups
Representations of Two Compact Groups
References
Index