Analytic functional calculus for two operators

الأصل · EN

Properties of the mappings align* C&1(2πi)²∫ᵧ₁∫ᵧ₂f(λ,μ)R₁,λC R₂,μdμdλ, C&12πi∫Γg(λ)R₁,λC R₂,λdλalign* are discussed; here R₁,₍·₎ and R₂,₍·₎ 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.