On the spectrum and eigenfunctions of the operator $(Vf)(x) = \int_0^{x^α} f(t) dt$

Ignat Domanov

doi:10.4064/bc75-0-8

paper

On the spectrum and eigenfunctions of the operator $(V f) (x) = \int_{0}^{x^{α}} f (t) d t$

arXiv:1301.4886 · doi:10.4064/bc75-0-8

Abstract

We find spectrum and eigenfunctions of the operator $(V f) (x) = \int_{0}^{x^{α}} f (t) d t$ in $L_{2} [0, 1]$

The results of this paper were included without a reference to it in the following paper: A. Montes, A. Rodríguez-Martínez, S. A. Shkarin; Spectral theory of Volterra-composition operators, Math. Z. 261(2009), no. 2, 431-472

On the spectrum and eigenfunctions of the operator (Vf)(x)=∫0xα​f(t)dt

Abstract

On the spectrum and eigenfunctions of the operator $(V f) (x) = \int_{0}^{x^{α}} f (t) d t$