Analytic functional calculus for two operators

2016/04/25 by V. G. Kurbatov, Kurbatov, V. G., И. В. Курбатова +3
Computer Science · Mathematics · #15A22 #34A30 #39B42 #47A60 #47A80 #47B49 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical methods for differential equations #Operator Algebras (math.OA) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1604.07393

openalex publication_date 2016/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Properties of the mappings Camp;↦\frac1(2πi)²∫_Γ1∫_Γ2f(λ,μ) R_{1, λ} C R_{2, μ} dμ dλ, Camp;↦\frac12πi∫_Γg(λ)R_{1, λ} C R_{2, λ} dλ are discussed; here R_{1, (⋅)} and R_{2, (⋅)} are pseudo-resolvents, i.~e., resolvents of bounded, unbounded, or multivalued linear operators, and f and g are analytic functions. Several applications are considered: a representation of the impulse response of a second order linear differential equation with operator coefficients, a representation of the solution of the Sylvester equation, and an exploration of properties of the differential of the ordinary functional calculus.

Citations

• Approximation of functions of large matrices with Kronecker structure

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