說明 
vii, 101 pages ; 26 cm 

text txt rdacontent 

unmediated n rdamedia 

volume nc rdacarrier 
系列 
Courant lecture notes in mathematics, 15299031 ; volume 31


Courant lecture notes in mathematics ; 31. 15299031

附註 
Includes bibliographical references (page 99) and index 

Preface  Fourier series  Fourier transforms on Rsuperscriptd  Singular integrals  Riesz transforms on Rsuperscriptd  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 nonAbelian 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 secondyear 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

