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書刊名： Fourier analysis : an introduction /stein elias m 1931

作者： Stein, Elias M., 1931-

出版社：

Princeton : Princeton University Press, c2003

ISBN：

069111384X : NT 9249780691113845

索書號： 515.2433 S819-3

套書內容： 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

稽核項：

xvi, 311 p. : ill. ; 24 cm

叢書名：

Princeton lectures in analysis ; 1

線上資源：

http://catdir.loc.gov/catdir/bios/prin051/2003103688.html http://catdir.loc.gov/catdir/description/prin051/2003103688.html http://catdir.loc.gov/catdir/toc/fy051/2003103688.html

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