The H^∞-functional calculus for bisectorial Clifford operators

2024/09/11 by Francesco Mantovani, Peter Schlösser, Mantovani, Francesco +1
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2409.07249

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this article is to introduce the H-infinity functional calculus for unbounded bisectorial operators in a Clifford module over the algebra R_n. While recent studies have focused on bounded operators or unbounded paravector operators, we now investigate unbounded fully Clifford operators and define polynomially growing functions of them. We first generate the omega-functional calculus for functions that exhibit an appropriate decay at zero and at infinity. We then extend to functions with a finite value at zero and at infinity. Finally, using a subsequent regularization procedure, we can define the H-infinity functional calculus for the class of regularizable functions, which in particular include functions with polynomial growth at infinity and, if T is injective, also functions with polynomial growth at zero.

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