Cargando…
Fourier analysis : an introduction
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | Libro |
| Lenguaje: | English |
| Publicado: |
Princeton, New Jersey :
Princeton University Press,
©2003.
|
| Colección: | Princeton lectures in analysis ;
1. |
| Materias: | |
| Acceso en línea: | http://catdir.loc.gov/catdir/toc/fy051/2003103688.html http://catdir.loc.gov/catdir/bios/prin051/2003103688.html http://catdir.loc.gov/catdir/description/prin051/2003103688.html |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ocm51569246 | ||
| 003 | UV# | ||
| 005 | 20170404141007.0 | ||
| 008 | 160602s2003 njua b 001 0 eng d | ||
| 999 | |c 299368 |d 299368 | ||
| 010 | |a 2003103688 | ||
| 015 | |2 bnb | ||
| 020 | |a 069111384X | ||
| 020 | |a 9780691113845 | ||
| 040 | |a UKM |b eng |c UKM |d DLC |d IXA |d BAKER |d NLGGC |d BTCTA |d LVB |d YDXCP |d UBA |d OCLCG |d OCLCQ |d CWI |d BDX |d OCLCF |d OCLCO |d OCLCQ |d MEAUC |d UV# |e rda | ||
| 050 | 0 | 0 | |a QA403.5 |b S83 2003 |
| 082 | 0 | 0 | |a 515/.2433 |2 22 |
| 100 | 1 | |a Stein, Elias M., |d 1931- |9 380955 | |
| 245 | 1 | 0 | |a Fourier analysis : |b an introduction |c / Elias M. Stein & Rami Shakarchi. |
| 260 | |a Princeton, New Jersey : |b Princeton University Press, |c ©2003. | ||
| 300 | |a xvi, 311 páginas : |b ilustraciones ; |c 24 cm. | ||
| 336 | |a texto |b txt |2 rdacontent | ||
| 337 | |a sin medio |b n |2 rdamedia | ||
| 338 | |a volumen |b nc |2 rdacarrier | ||
| 490 | 1 | |a Princeton lectures in analysis ; |v 1 | |
| 504 | |a Incluye bibliografía (páginas 301-303) e índice. | ||
| 505 | 0 | |a The Genesis of Fourier Analysis -- The vibrating string -- Derivation of the wave equation -- Solution to the wave equation -- Example: the plucked string -- The heat equation -- Derivation of the heat equation -- Steady-state heat equation in the disc -- Exercises -- Problem -- Basic Properties of Fourier Series -- Examples and formulation of the problem -- Main definitions and some examples -- Uniqueness of Fourier series -- Convulusions -- Good kernels -- Cesaro and Abel summability: applications to Fourier series -- Cesaro means and summation -- Fejer's theorem -- Abel means and summation -- The Poisson kernel and Dirichlet's problem in the unit disc -- Exercises -- Problems -- Convergence of Fourier Series -- Mean-square convergence of Fourier series -- Vector spaces and inner products -- Proof of mean-square convergence -- Return to pointwise convergence -- A local result -- A continuous function with diverging Fourier series -- Exercises -- Problems -- Some Applications of Fourier Series -- The isoperimetric inequality -- Weyl's equidistribution theorem -- A continuous but nowhere differentiable function -- The heat equation on the circle -- Exercises -- Problems -- The Fourier Transform on R -- Elementary theory of the Fourier transform -- Integration of functions on the real line -- Definition of the Fourier transform -- The Schwartz space -- The Fourier transform on S -- The Fourier inversion -- The Plancherel formula -- Extension to functions of moderate decrease -- The Weierstrass approximation theorem -- Applications to some partial differential equations -- The time-dependent heat equation on the real line -- The steady-state heat equation in the upper half-plane -- The Poisson summation formula -- Theta and zeta functions -- Heat kernels -- Poisson kernels -- The Heisenberg uncertainty principle -- Exercises -- Problems -- The Fourier Transform on Rd -- Preliminaries -- Symmetries -- Integration on Rd -- Elementary theory of the Fourier transform -- The wave equation in Rd x R -- Solution in terms of Fourier transforms -- The wave equation in R3 x R -- The wave equation in IR2 x R: descent -- Radial symmetry and Bessel functions -- The Radon transform and some of its applications -- The X-ray transform in R2 -- The Radon transform in R3 -- A note about plane waves -- Exercises -- Problems -- Finite Fourier Analysis -- Fourier analysis on Z(N) -- The group Z(N) -- Fourier inversion theorem and Plancherel identity on Z(N) -- The fast Fourier transform -- Fourier analysis on finite abelian groups -- Abelian groups -- Characters -- The orthogonality relations -- Characters as a total family -- Fourier inversion and Plancherel formula -- Exercises -- Problems -- Dirichlet's Theorem -- A little elementary number theory -- The fundamental theorem of arithmetic -- The infinitude of primes -- Dirichlet's theorem -- Fourier analysis, Dirichlet characters, and reduction of the theorem -- Dirichlet L-functions -- Proof of the theorem -- Logarithms -- L-functions -- Non-vanishing of the L-function -- Exercises -- Problems -- Appendix: Integration -- Definition of the Riemann integral -- Basic properties -- Sets of measure zero and discontinuities of integrable functions -- Multiple integrals -- The Riemann integral in Rd -- Repeated integrals -- The change of variables formula -- Spherical coordinates -- Improper integrals. Integration over Rd -- Integration of functions of moderate decrease -- Repeated integrals -- Spherical coordinates -- Notes and References -- Bibliography -- Symbol Glossary. | |
| 650 | 0 | |a Análisis de Fourier |9 2626 | |
| 700 | 1 | |a Shakarchi, Rami |9 366276 | |
| 830 | 0 | |a Princeton lectures in analysis ; |v 1. | |
| 856 | 4 | 1 | |u http://catdir.loc.gov/catdir/toc/fy051/2003103688.html |
| 856 | 4 | 2 | |u http://catdir.loc.gov/catdir/bios/prin051/2003103688.html |
| 856 | 4 | 2 | |u http://catdir.loc.gov/catdir/description/prin051/2003103688.html |
| 942 | |2 lcc |c LIBRO |6 _ | ||