The power boundedness and resolvent conditions for functions of the classical Volterra operator

• Autorzy: Yuri Lyubich
• Języki publikacji: EN

Abstrakty

EN

Let ϕ(z) be an analytic function in a disk |z| < ρ (in particular, a polynomial) such that ϕ(0) = 1, ϕ(z)≢ 1. Let V be the operator of integration in $L_{p}(0,1)$, 1 ≤ p ≤ ∞. Then ϕ(V) is power bounded if and only if ϕ'(0) < 0 and p = 2. In this case some explicit upper bounds are given for the norms of ϕ(V)ⁿ and subsequent differences between the powers. It is shown that ϕ(V) never satisfies the Ritt condition but the Kreiss condition is satisfied if and only if ϕ'(0) < 0, at least in the polynomial case.

Kategorie tematyczne

• 47A35: Ergodic theory
• 47G10: Integral operators
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 1
• Strony: 41-63

Daty

wydano

2010

Twórcy

autor

Yuri Lyubich

• Institute of Mathematics, Polish Academy of Sciences, Warszawa, Poland
• Technion, Haifa, Israel

Identyfikatory

DOI

10.4064/sm196-1-4