Introduction to the theory of Fourier integrals. (English) Zbl 0017.40404
Oxford: Clarendon Press. x, 390 p. (1937).
MathOverflow Questions:
Reference request: proofs of integrals presented in Erdélyi’s *Table of Integral Transforms*MSC:
| 42-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces |
| 44-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to integral transforms |
Keywords:
integral transforms; Fourier transform; Laplace transform; Mellin transform; convergence; summability; Fourier simple integrals; Fourier double integrals; Fourier transforms in \(L, L_2, L_p\); conjugate functions; Hilbert transforms; trigonometric integrals; general transforms; self-reciprocal functionDigital Library of Mathematical Functions:
§10.22(v) Hankel Transform ‣ §10.22 Integrals ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions§10.32(iii) Products ‣ §10.32 Integral Representations ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions
§1.14(ii) Fourier Cosine and Sine Transforms ‣ §1.14 Integral Transforms ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§1.14(i) Fourier Transform ‣ §1.14 Integral Transforms ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§1.14(iv) Mellin Transform ‣ §1.14 Integral Transforms ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§1.14(vii) Tables ‣ §1.14 Integral Transforms ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§1.14(v) Hilbert Transform ‣ §1.14 Integral Transforms ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§1.8(iv) Poisson’s Summation Formula ‣ §1.8 Fourier Series ‣ Topics of Discussion ‣ Chapter 1 Algebraic and Analytic Methods
§5.13 Integrals ‣ Properties ‣ Chapter 5 Gamma Function
