Glasnik Matematicki, Vol. 51, No. 2 (2016), 431-445.

PROPERTIES OF THE DISTRIBUTIONAL FINITE FOURIER TRANSFORM

Richard D. Carmichael

Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, U.S.A.
e-mail: carmicha@wfu.edu
This paper is dedicated to the memory of Professor Dr. Dragiša Mitrović of the University of Zagreb, Croatia.

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.

2010 Mathematics Subject Classification.   46F12, 46F20, 32A07, 32A26, 32A40.

Key words and phrases.   Analytic functions, distributions, finite Fourier transform, Cauchy integral.


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DOI: 10.3336/gm.51.2.10


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