Abstract
In a previous paper we introduced a family of differential-reflection operators ΛA , ϵ acting on smooth functions defined on R, where the spectral problem for the operators ΛA,ϵ has been studied. Here A is a Sturm-Liouville function with additional hypotheses and-1 ≤ ϵ ≤ 1. Via the eigenfunctions of ΛA,ϵ, we introduce in this paper a generalized Fourier transform fA,ϵ. An Lp-harmonic analysis for fA,ϵ is developed when 0 < p ≤ 2/1 + 1-ϵ2. In particular, an Lp-Schwartz space isomorphism theorem for fA,ϵ is proved.
Original language | English |
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Pages (from-to) | 43-63 |
Number of pages | 21 |
Journal | Advances in Pure and Applied Mathematics |
Volume | 8 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1 2017 |
Externally published | Yes |
Keywords
- Differential-reflection operators
- L-harmonic analysis
- generalized Fourier transform
ASJC Scopus subject areas
- Mathematics(all)