Properties of the distributional finite Fourier transform

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Carmichael, Richard D.; (2016)
  • Publisher: Croatian Mathematical Society and Department of Mathematics, University of Zagreb
  • Journal: Glasnik matematički,volume 51,issue 2 (issn: 0017-095X, eissn: 1846-7989)
  • Subject: Analytic functions; distributions; finite Fourier transform; Cauchy integral

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 in... View more
  • References (8)

    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.

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