Compactness criteria via Laguerre and Hankel transformations
\'A. P. Horv\'ath
TL;DR
This paper establishes new compactness criteria using Laguerre and Hankel transformations, extending classical theorems to these contexts and providing a deeper understanding of function space properties.
Contribution
It introduces Kolmogorov-Riesz and Pego-type theorems via Bessel and Laguerre translations and transformations, expanding the theoretical framework for compactness in harmonic analysis.
Findings
Proved Kolmogorov-Riesz type theorems using Laguerre translations.
Established Pego-type theorems with Hankel transformations.
Extended classical compactness criteria to new transform settings.
Abstract
The aim of this paper is to prove Kolmogorov-Riesz type theorems via Bessel and Laguerre translations, and Pego-type theorems by the corresponding transformations.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Mathematical functions and polynomials · Differential Equations and Boundary Problems