Fourier Series and Integrals

Description

Clickable bookmark; OCR layer; wide margin for note taking Preface/10,Black,notBold,notItalic,open,FitWidth,-1 Historical Introduction/12,Black,notBold,notItalic,open,FitWidth,-1 Chapter 1. Fourier Series/16,Black,notBold,notItalic,open,FitWidth,-1 1.1 The Lebesgue Integral/16,Black,notBold,notItalic,open,FitWidth,-1 1.2 The Geometry of L²(Q)/23,Black,notBold,notItalic,open,FitWidth,-1 1.3 The Geometry of L²(Q) Continued/33,Black,notBold,notItalic,open,TopLeftZoom,449,0,0.0 1.4 Square Summable Functions on the Circle and Their Fourier Series/40,Black,notBold,notItalic,open,TopLeftZoom,659,0,0.0 1.5 Summable Functions and Their Fourier Series/47,Black,notBold,notItalic,open,TopLeftZoom,998,0,0.0 1.6* Gibbs' Phenomenon/54,Black,notBold,notItalic,open,FitWidth,-1 1.7 Miscellaneous Applications/57,Black,notBold,notItalic,open,FitWidth,-1 1.8 Applications to the Partial Differential Equations of One-Dimensional Mathematical Physics/71,Black,notBold,notItalic,open,TopLeftZoom,641,0,0.0 1.9* More General Eigenfunction Expansions/83,Black,notBold,notItalic,open,FitWidth,-1 1.10 Several-Dimensional Fourier Series/92,Black,notBold,notItalic,open,FitWidth,-1 Chapter 2. Fourier Integrals/97,Black,notBold,notItalic,open,FitWidth,-1 2.1 Fourier Integrals/97,Black,notBold,notItalic,open,FitWidth,-1 2.2 Fourier Integrals for C^?_?(R1)/99,Black,notBold,notItalic,open,TopLeftZoom,365,0,0.0 2.3 Fourier Integrals for L²(R1): First Method/102,Black,notBold,notItalic,open,FitWidth,-1 2.4* Fourier Integrals for L²(R1}: Second Method/105,Black,notBold,notItalic,open,FitWidth,-1 2.5* Fourier Integrals for L²(R1): Third Method/108,Black,notBold,notItalic,open,FitWidth,-1 2.6 Fourier Integrals for L²(R1)/112,Black,notBold,notItalic,open,FitWidth,-1 2.7 Miscellaneous Applications/117,Black,notBold,notItalic,open,FitWidth,-1 2.8* Heisenberg's Inequality/127,Black,notBold,notItalic,open,FitWidth,-1 2.9* Band- and Time-Limited Functions/132,Black,notBold,notItalic,open,FitWidth,-1 2.10 Several-Dimensional Fourier Integrals/143,Black,notBold,notItalic,open,FitWidth,-1 2.11 Miscellaneous Applications of Several-Dimensional Fourier Integrals/145,Black,notBold,notItalic,open,FitWidth,-1 Chapter 3. Fourier Integrals and Complex Function Theory/155,Black,notBold,notItalic,open,FitWidth,-1 3.1 A Short Course in Function Theory/155,Black,notBold,notItalic,open,TopLeftZoom,492,0,0.0 3.2 Hardy's Theorem/167,Black,notBold,notItalic,open,FitWidth,-1 3.3 The Paley-Wiener Theorem/169,Black,notBold,notItalic,open,FitWidth,-1 3.4 Hardy Functions/172,Black,notBold,notItalic,open,FitWidth,-1 3.5* Hardy Functions and Filters/181,Black,notBold,notItalic,open,TopLeftZoom,259,0,0.0 3.6* Wiener-Hopf Factorization: Milne's Equation/187,Black,notBold,notItalic,open,FitWidth,-1 3.7* Spitter's Identity/195,Black,notBold,notItalic,open,TopLeftZoom,486,0,0.0 3.8* Hardy Functions in the Disk and Szegö's Theorem/198,Black,notBold,notItalic,open,TopLeftZoom,744,0,0.0 3.9* Polynomial Approximation: The Szász-Müntz Theorem/205,Black,notBold,notItalic,open,TopLeftZoom,639,0,0.0 3.10* The Prime Number Theorem/207,Black,notBold,notItalic,open,TopLeftZoom,555,0,0.0 Chapter 4. Fourier Series and Integrals on Groups/214,Black,notBold,notItalic,open,TopLeftZoom,218,0,0.0 4.1 Groups/214,Black,notBold,notItalic,open,TopLeftZoom,492,0,0.0 4.2 Fourier Series on the Circle/217,Black,notBold,notItalic,open,FitWidth,-1 4.3 Fourier Integrals on the Line/220,Black,notBold,notItalic,open,TopLeftZoom,800,0,0.0 4.4 Finite Commutative Groups/225,Black,notBold,notItalic,open,TopLeftZoom,674,0,0.0 4.5 Fourier Series on a Finite Commutative Group/228,Black,notBold,notItalic,open,TopLeftZoom,800,0,0.0 4.6* Gauss' Law of Quadratic Reciprocity/233,Black,notBold,notItalic,open,TopLeftZoom,695,0,0.0 4.7 Noncommutative Groups/237,Black,notBold,notItalic,open,TopLeftZoom,758,0,0.0 4.8 The Rotation Group/239,Black,notBold,notItalic,open,TopLeftZoom,496,0,0.0 4.9 Three Convolution Algebras/248,Black,notBold,notItalic,open,TopLeftZoom,233,0,0.0 4.10 Homomorphisrns of L¹(K/G/K)/250,Black,notBold,notItalic,open,TopLeftZoom,507,0,0.0 4.11 Spherical Functions Are Eigenfunctions of the Laplacian/253,Black,notBold,notItalic,open,TopLeftZoom,760,0,0.0 4.12 Spherical Functions Are Legendre Polynomials/256,Black,notBold,notItalic,open,TopLeftZoom,550,0,0.0 4.13 Spherical Harmonics/260,Black,notBold,notItalic,open,FitWidth,-1 4.14* Representations of SO(3)/266,Black,notBold,notItalic,open,TopLeftZoom,659,0,0.0 4.15* The Euclidean Motion Group/272,Black,notBold,notItalic,open,FitWidth,-1 4.16* SL(2,R) and the Hyperbolic Plane/284,Black,notBold,notItalic,open,TopLeftZoom,613,0,0.0 Additional Reading/293,Black,notBold,notItalic,open,FitWidth,-1 Bibliography/244,Black,notBold,notItalic,open,FitWidth,-1 Index/300,Black,notBold,notItalic,open,FitWidth,-1