A generalization of the Kreiss Matrix Theorem

作者：Raouafi Samir^*

来源：Linear Algebra and Its Applications, 2018, 549: 86-99.

DOI：10.1016/j.laa.2018.03.011

• Kreiss Matrix Theorem
• Resolvent
• Markov function
• Faber polynomial

Let sa be a compact subset of the complex plane such that its complement is simply connected in the extended complex plane. Suppose A is a linear bounded operator in a Hilbert space, with spectrum sigma(A) subset of Omega. If Omega is symmetric with respect to the real line and f is a Markov function, we show that
parallel to f(A)parallel to <= e C K(Omega) parallel to f parallel to(Omega),
where K(Omega) is the Kreiss constant with respect to Omega and C is a constant. We also present other extensions of the Kreiss Matrix Theorem to arbitrary holomorphic functions.

• 出版日期2018-7-15