An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain

• Autorzy: Gil` M. I.

Identyfikatory

DOI

10.1515/JAA-2013-014

• Języki publikacji: EN

Abstrakty

EN

We consider the operator T defined by (T f)(x)=(Sf)(x)+q(x)f(x), x ∈ Ω, where Ω ⊂ Rⁿ is an unbounded domain, S is a positive definite selfadjoint operator defined on a domain Dom (S) ⊂ L²(Ω) and q(x) is a bounded complex measurable function with the property Im q(x) ∈ L^ν(Ω) for a ν ∈ (1, ∞). We derive an estimate for the norm of the resolvent of T. In addition, we prove that T is invertible, and the inverse operator T^-1 is a sum of a normal operator and a quasinilpotent one, having the same invariant subspaces. By the derived estimate, spectrum perturbations are investigated. Moreover, a representation for the resolvent of T by the multiplicative integral is established. As examples, we consider the Schrödinger operators on the positive half-line and orthant.

Słowa kluczowe

EN

ordinary differential operators; partial differential operators; resolvent; spectrum perturbations

PL

operator różniczkowy; rezolwenta; perturbacje

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2013
• Tom: Vol. 19, nr 2
• Strony: 231--246
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Gil` M. I.

• Department of Mathematics, Ben Gurion University, P.O. Box 653, Beer-Sheva 84105, Israel

Bibliografia

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