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WINTER 2014 On the half-Hartley transform, its iteration and compositions with Fourier transforms
S. Yakubovich
J. Integral Equations Applications 26(4): 581-608 (WINTER 2014). DOI: 10.1216/JIE-2014-26-4-581


Employing the generalized Parseval equality for the Mellin transform and elementary trigonometric formulas, the iterated Hartley transform on the nonnegative half-axis (the iterated half-Hartley transform) is investigated in $L_2$. Mapping and inversion properties are discussed, its relationship with the iterated Stieltjes transform is established. Various compositions with the Fourier cosine and sine transforms are obtained. The results are applied to the uniqueness and universality of the closed form solutions for certain new singular integral and integro-functional equations. \bigskip


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S. Yakubovich. "On the half-Hartley transform, its iteration and compositions with Fourier transforms." J. Integral Equations Applications 26 (4) 581 - 608, WINTER 2014.


Published: WINTER 2014
First available in Project Euclid: 9 January 2015

zbMATH: 1307.44008
MathSciNet: MR3299832
Digital Object Identifier: 10.1216/JIE-2014-26-4-581

Primary: 44A15 , 44A35 , 45E05 , 45E10

Keywords: Fourier transforms , Hartley transform , Hilbert transform , integro-functional equations , Mellin transform , Plancherel theorem , Singular integral equations , Stieltjes transform

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

Vol.26 • No. 4 • WINTER 2014
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