Work

The Sneddon ℛ-Transform and Its Inverse over Lebesgue Spaces

Year: 2026

Type: article

Abstract: We study the Sneddon R-transform and its inverse in the setting of Lebesgue spaces. Generated by the mixed trigonometric kernel xcos(xt)+hsin(xt), the R-transform acts as a unifying operator for sine- and cosine-type integral transforms. Boundedness, continuity, and weighted Lp-estimates are established in an appropriate Banach space framework, together with Parseval–Goldstein type identities. Initial and final value theorems are derived for generalized functions in Zemanian-type spaces, yielding precise asymptotic behaviour at the origin and at infinity. A finite-interval theory is also developed, leading to polynomial growth estimates and final value theorems for the finite R-transform.

Source: Axioms

DOI: 10.3390/axioms15010063

Authors: Hari Mohan Srivastava, Emilio R. Negrín, Jeetendrasingh Maan

Institutions: Chung Yuan Christian University, China Medical University, University of Victoria, Kyung Hee University, China Medical University Hospital, UniNettuno University, Azerbaijan University, Universidad de La Laguna, National Institute of Technology Hamirpur

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

OpenAlex ID: W7124455944

FWCI: 12.19

Cites: 8

Cited by: 1

Related to: