## Journal of Integral Equations and Applications

### On the half-Hartley transform, its iteration and compositions with Fourier transforms

S. Yakubovich

#### Abstract

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

#### Article information

Source
J. Integral Equations Applications, Volume 26, Number 4 (2014), 581-608.

Dates
First available in Project Euclid: 9 January 2015

https://projecteuclid.org/euclid.jiea/1420812886

Digital Object Identifier
doi:10.1216/JIE-2014-26-4-581

Mathematical Reviews number (MathSciNet)
MR3299832

Zentralblatt MATH identifier
1307.44008

#### Citation

Yakubovich, S. On the half-Hartley transform, its iteration and compositions with Fourier transforms. J. Integral Equations Applications 26 (2014), no. 4, 581--608. doi:10.1216/JIE-2014-26-4-581. https://projecteuclid.org/euclid.jiea/1420812886

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