On the half-Hartley transform, its iteration and compositions with Fourier transforms. (English) Zbl 1307.44008
Summary: 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.
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 44A35 | Convolution as an integral transform |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 45E05 | Integral equations with kernels of Cauchy type |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
Keywords:
Hartley transform; Mellin transform; Fourier transforms; Hilbert transform; Stieltjes transform; Plancherel theorem; singular integral equations; integro-functional equations; Parseval equalityReferences:
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