Harmonic analysis is the study of functions by decomposing them into components that are special functions, says Varadhan, and he considers here only those aspects of the vast field that were part of the course he taught at the Courant Institute during 2000 and 2019. He covers Fourier series, Fourier transforms, singular integrals, Riesz transforms, Sobolev spaces, Hardy spaces, bounded mean oscillation, elliptic partial differential equations, Banach algebras and Wiener's Theorem, compact groups, and representations of two compact groups. Annotation ©2022 Ringgold, Inc., Portland, OR (protoview.com)
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Paperback. Condizione: New. 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. Codice articolo LU-9781470465070
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Paperback. Condizione: New. 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. Codice articolo LU-9781470465070
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Condizione: New. Harmonic Analysis is an important tool that plays a vital role in many areas of mathematics as well as applications. The subject is vast, and this book covers only a selection of topics, such as Fourier series and Fourier transforms of functions, and issues. Codice articolo 628915203
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