Harmonic analysis /
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....
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
[2022]
Providence, Rhode Island : [2022] |
| Series: | Courant lecture notes in mathematics ;
v. 31 Courant lecture notes in mathematics volume 31. |
| Subjects: |
Harmonic analysis on Euclidean spaces
> Instructional exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
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| 100 | 1 | |a Varadhan, S. R. S., |e author | |
| 245 | 1 | 0 | |a Harmonic analysis / |c S.R.S. Varadhan, Courant Institute of Mathematical Sciences, New York University |
| 263 | |a 2202 | ||
| 264 | 1 | |a Providence : |b American Mathematical Society, |c [2022] | |
| 264 | 1 | |a Providence, Rhode Island : |b American Mathematical Society, |c [2022] | |
| 264 | 4 | |c ©2022 | |
| 300 | |a 1 online resource | ||
| 300 | |a 1 online resource (pages cm.) : | ||
| 300 | |a 1 online resource (pages cm.) | ||
| 300 | |a 1 online resource (vii, 101 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 338 | |a volume |b nc |2 rdacarrier | ||
| 347 | |a text file |2 rdaft | ||
| 490 | 0 | |a Courant Lecture Notes, |x 2472-4467 ; |v v. 31 | |
| 490 | 0 | |a Courant lecture notes, |x 1529-9031 ; |v volume 31 | |
| 490 | 1 | |a Courant lecture notes, |x 1529-9031 ; |v volume 31 | |
| 504 | |a Includes bibliographical references and index | ||
| 505 | 0 | |a Intro -- Preface -- Chapter 1. Fourier Series -- 1.1. Introduction -- 1.2. Convergence of Fourier series -- 1.3. Special case =2 -- 1.4. Higher dimensions -- 1.5. Maximal inequality -- 1.6. Exercises -- Chapter 2. Fourier Transforms on ^{ } -- 2.1. Smooth rapidly decaying functions -- 2.2. Exercises -- Chapter 3. Singular Integrals -- 3.1. Interpolation theorems -- 3.2. Weak type inequality -- 3.3. Exercises -- Chapter 4. Riesz Transforms on ^{ } -- 4.1. Singular integrals on ^{ } -- 4.2. Riesz kernels -- 4.3. Exercises -- Chapter 5. Sobolev Spaces -- 5.1. Generalized derivatives | |
| 505 | 0 | 0 | |t Fourier Series |t Fourier Transforms on $\mathbb {R}^d$ |t Singular Integrals |t Riesz Transforms on $\mathbb {R}^d$ |t Sobolev Spaces |t Hardy Spaces |t Bounded Mean Oscillation |t Elliptic PDEs |t Banach Algebras and Wiener's Theorem |t Compact Groups |t Representations of Two Compact Groups |
| 505 | 8 | |a 10.1. Haar measure -- 10.2. Representations of a group -- 10.3. Representations of a compact group -- Chapter 11. Representations of Two Compact Groups -- 11.1. Representations of the permutation group -- 11.2. Representations of SO(3) -- References -- Index | |
| 505 | 8 | |a 5.2. Approximation theorems -- 5.3. Embedding theorems -- 5.4. Trace and extension theorems -- 5.5. Fractional derivatives -- 5.6. Generalized functions -- 5.7. Exercises -- Chapter 6. Hardy Spaces -- 6.1. Stationary Gaussian processes -- 6.2. Hardy spaces -- 6.3. Inner and outer functions -- 6.4. Connection to prediction theory -- 6.5. Exercises -- Chapter 7. Bounded Mean Oscillation -- 7.1. Functions of bounded mean oscillation -- 7.2. Duality of and ₁ -- 7.3. Exercises -- Chapter 8. Elliptic PDEs -- Chapter 9. Banach Algebras and Wiener's Theorem -- Chapter 10. Compact Groups | |
| 506 | |a ProQuest Non-Linear Lending |f PQENL | ||
| 506 | |a Restricted for use by site license. | ||
| 520 | |a 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 | ||
| 533 | |a Electronic reproduction |b Providence, Rhode Island : |c American Mathematical Society. |d 2022 | ||
| 538 | |a Mode of access : World Wide Web | ||
| 588 | |a Description based on online resource; title from digital title page (viewed on July 17, 2022) | ||
| 588 | |a Description based on print version record | ||
| 650 | 0 | |a Harmonic analysis | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable |2 msc | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables |2 msc | |
| 650 | 7 | |a Harmonic analysis on Euclidean spaces -- Instructional exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces |2 msc | |
| 650 | 7 | |a Harmonic analysis |2 fast | |
| 650 | 7 | |a Probability theory and stochastic processes -- Stochastic processes -- Prediction theory (aspects of stochastic processes) |2 msc | |
| 655 | 0 | |a Electronic books | |
| 776 | 0 | |i Print version: |a Varadhan, S. R. S., |t Harmonic analysis / |w (DLC) 2021044384 |x 1529-9031 |z 9781470465070 | |
| 776 | 0 | 8 | |c Original |z 9781470465070 |z 1470465078 |w (DLC) 2021044384 |w (OCoLC)1284918663 |
| 776 | 0 | 8 | |i Print version: |a Varadhan, S. R. S |t Harmonic Analysis |d Providence : American Mathematical Society,c2022 |z 9781470465070 |
| 776 | 0 | 8 | |i Print version: |a Varadhan, S. R. S., |t Harmonic analysis /. |z 9781470465070 |z 1470465078 |w (DLC) 2021044384 |
| 830 | 0 | |a Courant lecture notes in mathematics ; |v v. 31 | |
| 830 | 0 | |a Courant lecture notes in mathematics |x 1529-9031 ; |v volume 31. | |
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