Harmonic analysis / S.R.S. Varadhan, Courant Institute.

• 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. 

Ämnesord

Harmonic analysis.  (LCSH)

Fourier Analysis  (MeSH)

Analyse harmonique.  (Vedettes-matière)

Harmonic analysis.  (fast)

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)

Målgrupp

"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.

Klassifikation

QA403 (LCC)

515/.2433 (DDC)

42-01 (msc)

Tdbf (kssb/8 (machine generated))