Hermite expansions of $C_0$-groups and cosine functions

TL;DR

This paper develops vector-valued Hermite expansions to approximate $C_0$-groups and cosine functions, providing convergence rate estimates and comparisons with existing methods, supported by illustrative examples.

Contribution

It introduces a novel Hermite expansion approach for $C_0$-groups and cosine functions, including convergence analysis and practical illustrations.

Findings

Hermite expansions effectively approximate $C_0$-groups and cosine functions.

Convergence rates are established and compared with other approximation methods.

Examples demonstrate the practical applicability of the Hermite expansions.

Abstract

In this paper we introduce vector-valued Hermite expansions to approximate one-parameter operator families such as $C_0$-groups and cosine functions. In both cases we estimate the rate of convergence of these Hermite expansions to the related family and compare with other known approximations. Finally we illustrate our results with particular examples of $C_0$-groups and cosine functions and their Hermite expansions.