C₀-semigroups and resolvent operators approximated by Laguerre\n expansions

2013/11/29 by Luciano Abadías, Abadias, Luciano, Pedro J. Miana +1
Engineering · Mathematics · #33C45 #41A35 #47A60 #47D06 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Primarly #Secondary #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1311.7542

openalex publication_date 2013/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce Laguerre expansions to approximate vector-valued\nfunctions expanding on the well-known scalar theorem. We apply this result to\napproximate C₀-semi -groups and resolvent operators in abstract Banach\nspaces. We study certain Laguerre functions, its Laplace transforms and the\nconvergence of Laguerre series in Lebesgue spaces. The concluding section of\nthis paper is devote to consider some examples of C₀-semigroups: shift,\nconvolution and holomorphic semigroups where some of these results are\nimproved.\n

Citations

• Mean Convergence of Expansions in Laguerre and Hermite Series

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