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.

Original languageEnglish
Pages (from-to)175-186
Number of pages12
JournalMathematical Physics Analysis and Geometry
Volume11
Issue number2
DOIs
StatePublished - 1 May 2008

Keywords

  • Comparison
  • Hille-Tamarkin matrices
  • Infinite matrices
  • Matrix valued functions
  • Monotone matrices
  • Norm estimates
  • Perturbations
  • Positivity

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