Estimates for functions of two commuting infinite matrices and applications (original) (raw)

Abstract

We consider a matrix valued function of two infinite commuting matrices generating bounded operators in a Banach space. Sharp estimates for the norm and entries are derived. Applications of the obtained estimates to differential equations are also discussed. Keywords Functions of infinite commuting matrices • Norm estimates • Partial differential equations in a Banach space Mathematics Subject Classification (2000) 47A56 • 47A60 • 35L90 • 15-99 This research was supported by the Kamea Fund of the Israel.

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