The Sneddon ℛ-Transform and Its Inverse over Lebesgue Spaces
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.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Advanced Harmonic Analysis Research
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Axioms
- Publisher
- MDPI AG
- Volume
- 15
- Issue
- 1
- Pages
- 63–63
- Publication date
- 16 January 2026
- Language
- EN