Abstract Volterra integral equations of wave type with almost sectorial operators

2025/09/05 by Joel E. Restrepo, Restrepo, Joel E.
Mathematics · #34K08 #45D05 #65J08 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2509.05229

openalex publication_date 2025/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for the latter type of operators to construct a general class of bounded linear operators that in particular contains the propagators (solution operators) of the considered equations. Some properties of this family of operators are also given.

Citations

• Functional calculi for sectorial operators and related function theory
• THE GENERALIZED BESSEL FUNCTION OF ORDER GREATER THAN ONE

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