Bounds for Analytical Functions of Matrices

Autor:	Michel Crouzeix
Rok vydání:	2004
Předmět:	Complex-valued function Algebra and Number Theory Effective domain Bounded function Mathematical analysis Proper convex function Function (mathematics) Square matrix Analysis Domain (mathematical analysis) Mathematics Analytic function
Zdroj:	Integral Equations and Operator Theory. 48:461-477
ISSN:	0378-620X
DOI:	10.1007/s00020-002-1188-6
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::52679c07cc281dbcf564a8c609df1e74 https://doi.org/10.1007/s00020-002-1188-6 Zobrazit plný text záznamu Full text from SpringerLink