publication . Article . Other literature type . 2016

Properties of the distributional finite Fourier transform

Richard D. Carmichael;
Open Access
  • Published: 01 Jan 2016 Journal: Glasnik Matematicki, volume 51, pages 431-445 (issn: 0017-095X, Copyright policy)
  • Publisher: University of Zagreb, Department of Mathematics
Abstract
The analytic functions in tubes which obtain the distributional finite Fourier transform as boundary value are shown to have a strong boundedness property and to be recoverable as a Fourier-Laplace transform, a distributional finite Fourier transform, and as a Cauchy integral of a distribution associated with the boundary value.
Persistent Identifiers
Subjects
free text keywords: Analytic functions; distributions; finite Fourier transform; Cauchy integral, Fourier inversion theorem, Fourier transform, symbols.namesake, symbols, Short-time Fourier transform, Fourier transform on finite groups, Mathematical analysis, Discrete Fourier transform (general), Discrete Fourier transform, Fractional Fourier transform, Mathematics, Non-uniform discrete Fourier transform

F [φ(t); x] = Z h(z) = Z We now obtain (5). Let C′ ⊂ C, m > 0, and z = x + iy ∈ T (C′, m).

For the given C′ ⊂ C and m > 0 choose b > 0 such that 0 < b < m,

[4] R. D. Carmichael and D. Mitrovi´c, Distributions and analytic functions, Longman Scientific and Technical, Harlow, 1989.

[5] R. E. Edwards, Functional analysis: theory and applications, Holt, Rinehart and Winston, New York, 1965.

[6] L. Schwartz, Th´eorie des distributions, Hermann, Paris, 1966.

[7] B. Simon, The P(φ)2 Euclidean (Quantum) Field Theory, Princeton University Press, Princeton, NJ, 1974.

[8] R. F. Streater and A. S. Wightman, PCT, spin and statistics, and all that, W. A. Benjamin, Inc., New York, 1964.

[9] V. S. Vladimirov, Methods of the theory of functions of many complex variables, M.I.T. Press, Cambridge, 1966.

Any information missing or wrong?Report an Issue