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Fourier integrals

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1: 1.15 Summability Methods
§1.15(v) Summability of Fourier Integrals
Poisson Kernel
Fejér Kernel
2: 2.3 Integrals of a Real Variable
For the Fourier integralThen …
3: 7.14 Integrals
Fourier Transform
4: 1.17 Integral and Series Representations of the Dirac Delta
§1.17(ii) Integral Representations
Formal interchange of the order of integration in the Fourier integral formula ((1.14.1) and (1.14.4)): …
1.17.17 1 2 π k = - e - i k a ( - π π ϕ ( x ) e i k x d x ) = ϕ ( a ) ,
5: Peter L. Walker
Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. …
6: Bibliography T
  • I. C. Tang (1969) Some definite integrals and Fourier series for Jacobian elliptic functions. Z. Angew. Math. Mech. 49, pp. 95–96.
  • E. C. Titchmarsh (1986a) Introduction to the Theory of Fourier Integrals. Third edition, Chelsea Publishing Co., New York.
  • 7: 13.10 Integrals
    §13.10(iv) Fourier Transforms
    8: 13.23 Integrals
    §13.23(ii) Fourier Transforms
    9: Bibliography C
  • H. S. Carslaw (1930) Introduction to the Theory of Fourier’s Series and Integrals. 3rd edition, Macmillan, London.
  • W. W. Clendenin (1966) A method for numerical calculation of Fourier integrals. Numer. Math. 8 (5), pp. 422–436.
  • 10: 6.16 Mathematical Applications
    §6.16(i) The Gibbs Phenomenon
    Consider the Fourier series … Compare Figure 6.16.1. … It occurs with Fourier-series expansions of all piecewise continuous functions. … …