The norms and singular numbers of polynomials of the classical Volterra operator in L₂(0,1)

• Autorzy: Yuri Lyubich , Dashdondog Tsedenbayar
• Języki publikacji: EN

Abstrakty

EN

The spectral problem (s²I - ϕ(V)*ϕ(V))f = 0 for an arbitrary complex polynomial ϕ of the classical Volterra operator V in L₂(0,1) is considered. An equivalent boundary value problem for a differential equation of order 2n, n = deg(ϕ), is constructed. In the case ϕ(z) = 1 + az the singular numbers are explicitly described in terms of roots of a transcendental equation, their localization and asymptotic behavior is investigated, and an explicit formula for the ||I + aV||₂ is given. For all a ≠ 0 this norm turns out to be greater than 1.

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: 199
• Numer: 2
• Strony: 171-184

Daty

wydano

2010

Twórcy

autor

Yuri Lyubich

• Technion, Haifa 32000, Israel

autor

Dashdondog Tsedenbayar

• Department of Mathematics, Mongolian University of Science and Technology, P.O. Box 46/520, Ulaanbaatar, Mongolia

Identyfikatory

DOI

10.4064/sm199-2-3