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作者 Varadhan, S. R. S., author
書名 Harmonic analysis / S.R.S. Varadhan, Courant Institute
出版項 Providence, Rhode Island : American Mathematical Society, [2022]
國際標準書號 9781470465070
book jacket
館藏地 索書號 處理狀態 OPAC 訊息 條碼
 數學所圖書室  QA403 V35 2022    到期 08-01-23    30340200571895
說明 vii, 101 pages ; 26 cm
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Courant lecture notes in mathematics, 1529-9031 ; volume 31
Courant lecture notes in mathematics ; 31. 1529-9031
附註 Includes bibliographical references (page 99) and index
Preface -- Fourier series -- Fourier transforms on R-superscript-d -- Singular integrals -- Riesz transforms on R-superscript-d -- Sobolev spaces -- Hardy spaces -- Bounded mean oscillation -- Elliptic PDEs -- Banach algebras and Wiener's Theorem -- Compact groups -- Representations of two compact groups
"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)."--Page 4 of printed paper wrapper
"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."--Page 4 of printed paper wrapper
主題 Harmonic analysis
Fourier Analysis
Analyse harmonique
Harmonic analysis. fast (OCoLC)fst00951490
Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces. msc
Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable. msc
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables. msc
Probability theory and stochastic processes -- Stochastic processes -- Prediction theory (aspects of stochastic processes). msc
Alt Author Courant Institute of Mathematical Sciences
American Mathematical Society
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