Generalized upper and lower Legendre conjugates for Braun-Meise-Taylor weight functions

TL;DR

This paper introduces generalized Legendre conjugates for Braun-Meise-Taylor weight functions, analyzing their impact on associated weight matrices and extending results on the resolvent operator's properties in Gelfand-Shilov spaces.

Contribution

It develops a new framework of generalized conjugates for weight functions, expanding the understanding of weighted space operators and their continuity properties.

Findings

Generalized conjugates affect the structure of weight matrices.

Extended the range and continuity results of the resolvent operator.

Provided concrete applications to Gelfand-Shilov spaces.

Abstract

We apply recent knowledge and techniques of the new generalized upper and lower Legendre conjugates to the theory of weight functions in the sense of Braun-Meise-Taylor and study in detail the effects on the corresponding associated weight matrices. An immediate and concrete application of the main statements is also provided. More precisely, we generalize a very recent result concerning the continuity and the range of the resolvent operator when being considered on weighted spaces of globally defined functions of Gelfand-Shilov type.