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

Yuri Lyubich, and Dashdondog Tsedenbayar. "The norms and singular numbers of polynomials of the classical Volterra operator in L₂(0,1)." Studia Mathematica 199.2 (2010): 171-184. <http://eudml.org/doc/285437>.

@article{YuriLyubich2010,
abstract = {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.},
author = {Yuri Lyubich, Dashdondog Tsedenbayar},
journal = {Studia Mathematica},
keywords = {Volterra operator; singular numbers; boundary value problem},
language = {eng},
number = {2},
pages = {171-184},
title = {The norms and singular numbers of polynomials of the classical Volterra operator in L₂(0,1)},
url = {http://eudml.org/doc/285437},
volume = {199},
year = {2010},
}

TY - JOUR
AU - Yuri Lyubich
AU - Dashdondog Tsedenbayar
TI - The norms and singular numbers of polynomials of the classical Volterra operator in L₂(0,1)
JO - Studia Mathematica
PY - 2010
VL - 199
IS - 2
SP - 171
EP - 184
AB - 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.
LA - eng
KW - Volterra operator; singular numbers; boundary value problem
UR - http://eudml.org/doc/285437
ER -