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Estimates for Entries of Matrix Valued Functions of Infinite Matrices

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Abstract

Sharp upper estimates for the absolute values of entries of matrix valued functions of infinite matrices, as well as two sided estimates for the entries of matrix valued functions of infinite M-matrices (monotone matrices) are derived. They give us bounds for the lattice norms of matrix valued functions and positivity conditions for functions of M-matrices. In addition, some results on perturbations and comparison of matrix functions are proved. Applications of the obtained estimates to the Hille-Tamarkin matrices and differential equations are also discussed.

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Authors and Affiliations

  1. Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel

    M. I. Gil’

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  1. M. I. Gil’
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Correspondence to M. I. Gil’.

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This research was supported by the Kamea fund of the Israel

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Gil’, M.I. Estimates for Entries of Matrix Valued Functions of Infinite Matrices. Math Phys Anal Geom 11, 175–186 (2008). https://doi.org/10.1007/s11040-008-9046-7

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  • DOI: https://doi.org/10.1007/s11040-008-9046-7

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