Journal of Integral Equations and Applications

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

S. Yakubovich

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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

Permanent link to this document
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

Subjects
Primary: 44A15: Special transforms (Legendre, Hilbert, etc.) 44A35: Convolution 45E05: Integral equations with kernels of Cauchy type [See also 35J15] 45E10: Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]

Keywords
Hartley transform Mellin transform Fourier transforms Hilbert transform Stieltjes transform Plancherel theorem singular integral equations integro-functional equations

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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References

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