Introduction to harmonic analysis
Ricardo A. Sáenz
Bok · Engelsk · 2023
| Omfang | xv, 279 sider : illustrasjoner, figurer
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| Opplysninger | Preface -- Chapter 1. Motivation and preliminaries -- Chapter 2. Basic properties -- Chapter 3. Fourier series -- Chapter 4. Poisson kernel in the half-space -- Chapter 5. Measure theory in Euclidean space -- Chapter 6. Lebesgue integral and Lebesgue spaces -- Chapter 7. Maximal functions -- Chapter 8. Fourier transform -- Chapter 9. Hilbert transform -- Chapter 10. Mathematics of fractals -- Chapter 11. The Laplacian on the Sierpiński gasket -- Chapter 12. Eigenfunctions of the Laplacian -- Chapter 13. Harmonic functions on post-critically finite sets -- Appendix A. Some results from real analysis.. - This book gives a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure theory, Lebesgue integration and approximation theorems.The book motivates the study of harmonic functions by describing the Dirichlet problem, and discussing examples such as solutions to the heat equation in e.
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| Emner | Harmonic analysis.
Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Convergence and absolute convergence of Fourier and trigonometric series. Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series. Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type. Vis mer... Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables -- Maximal functions, Littlewood-Paley theory.
Measure and integration -- Classical measure theory -- Fractals. Measure and integration -- Classical measure theory -- Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence. Potential theory -- Higher-dimensional theory -- Boundary behavior. Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions. Potential theory -- Higher-dimensional theory -- Integral representations, integral operators, integral equations methods. harmoni-analyse Fourier-rekker matematikk |
| Dewey | |
| ISBN | 147047199X. - 9781470471996
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| ISBN(galt) |