On upper estimates for approximation numbers of a Laplace type transformation
Elena P. Ushakova
TL;DR
This paper investigates the approximation properties of a Laplace-type integral operator between Lebesgue spaces, providing conditions for Schatten class membership and deriving upper bounds for approximation numbers.
Contribution
It introduces new sufficient conditions for the operator to belong to Schatten classes and offers asymptotic estimates for its approximation numbers.
Findings
Conditions for Schatten class inclusion derived
Upper asymptotic estimates for approximation numbers established
Analysis focused on Laplace-type integral operators
Abstract
We deal with a real valued integral operator L of Laplace transformation type acting between Lebesgue spaces on the semi-axis. Sufficient conditions for belonging L to Schatten type classes are obtained. Some upper asymptotic estimates for the approximation numbers of L are also given.
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