On the spectrum of the operator which is a composition of integration and substitution

• Autorzy: Ignat Domanov
• Języki publikacji: EN

Abstrakty

EN

Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator $V_{ϕ} : f(x) ↦ ∫_{0}^{ϕ(x)} f(t)dt$ be defined on L₂[0,1]. We prove that $V_{ϕ}$ has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator $V_{ϕ}$ always equals 1.

Kategorie tematyczne

• 45C05: Eigenvalue problems
• 47A75: Eigenvalue problems
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 185
• Numer: 1
• Strony: 49-65

Daty

wydano

2008

Twórcy

autor

Ignat Domanov

• Institute of Applied Mathematics and Mechanics, Ukrainian National Academy of Sciences, R. Luxemburg St. 74, 83114 Donetsk, Ukraine
• Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic

Identyfikatory

DOI

10.4064/sm185-1-3