OSCILLATORY SINGULAR SPECIAL FUNCTION TRANSFORM

Abdul Hamid Ganie

doi:10.11948/20260010

2026 Volume 16 Issue 5

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Abdul Hamid Ganie. OSCILLATORY SINGULAR SPECIAL FUNCTION TRANSFORM[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2474-2496. doi: 10.11948/20260010

Citation:

Abdul Hamid Ganie. OSCILLATORY SINGULAR SPECIAL FUNCTION TRANSFORM[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2474-2496. doi: 10.11948/20260010

OSCILLATORY SINGULAR SPECIAL FUNCTION TRANSFORM

Abdul Hamid Ganie^1, ,

1.
Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia

Corresponding author: Email: a.ganie@seu.edu.sa(A. H. Ganie)

Abstract

Abstract

We introduce a new class of integral transforms, called the Oscillatory Singular Special Function Transform (OSSFT), whose kernels combine algebraic singularities, nonlinear oscillatory phases, and special-function components of Mittag–Leffler type. Fundamental properties of the OSSFT are established, including boundedness on weighted Lebesgue spaces, stability, compactness, and smoothing effects. Under suitable symmetry and decay conditions, a Plancherel-type theorem and Heisenberg-type uncertainty inequalities are proved. The compactness of the associated operators further yields spectral discreteness and Sobolev regularity of eigenfunctions.
- Oscillatory integral transforms /
- singular kernels /
- special functions /
- Mittag-Leffler functions /
- weighted Lebesgue spaces
MSC: 44A15, 42B10, 47B34, 26A33, 35S30, 46E30

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References

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