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Bounds for Analytical Functions of Matrices

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Abstract.

If f is an analytic function bounded on a convex domain of the complex plane and A a square matrix whose spectrum is included in this domain, the function f(A) is well defined. In this paper we study bounds for ||f(A)|| uniform with respect to the functions f bounded by 1, and uniform with respect to the matrices A whose the numerical ranges are included in the domain. We show that these bounds are attained and give explicit formulae in some 2-dimensional cases.

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  1. Institut de Recherche Mathématique de Rennes, UMR 6625, Université de Rennes 1, Campus de Beaulieu, Rennes Cedex, 35042, France

    Michel Crouzeix

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  1. Michel Crouzeix
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Correspondence to Michel Crouzeix.

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Crouzeix, M. Bounds for Analytical Functions of Matrices. Integr. equ. oper. theory 48, 461–477 (2004). https://doi.org/10.1007/s00020-002-1188-6

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  • DOI: https://doi.org/10.1007/s00020-002-1188-6

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