Deformed Hankel transform of Dini – Lipschitz functions

A.  Elgargati; M. El  Loualid; R. Daher

doi:10.37863/umzh.v74i8.6134

A. Elgargati Laboratory Fundamental and Applied Mathematics, Univ. Hassan II, Casablanca, Morocco
M. El Loualid Chouaib Doukkali Univ. El Jadida, Nat. School Applied Sci., Sci. Engineer Lab. Energy, El Jadida,Morocco https://orcid.org/0000-0002-2915-1772
R. Daher Laboratory Fundamental and Applied Mathematics, Univ. Hassan II, Casablanca, Morocco

DOI: https://doi.org/10.37863/umzh.v74i8.6134

Keywords: Deformed Hankel transfor, Titchmarsh theore, Symmetric differenc

Abstract

UDC 517.5

By using a generalized symmetric difference $\Delta_{h}^{m}$ of order $m$ and step $h>0,$ we obtain an analog of the Titchmarsh theorems [Introduction to the theory of Fourier integrals, Oxford Univ. Press (1948)] (Theorems 84 and 85) for the deformed Hankel transform.
We also provide a further extension of the theorem cited above for functions in $L_k^{p}$ with an abstract deformed Hankel – Dini – Lipschitz condition.

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