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An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain
-
Michael I. Gil'
Published/Copyright:
October 8, 2013
Abstract.
We consider the operator T defined by
, 
,
where 
is an unbounded domain, S is
a positive definite selfadjoint operator defined
on a domain 
and 
is a bounded complex measurable function with the property 
for a 
.
We derive an estimate for the norm of the resolvent of T. In addition, we prove that T is invertible, and the inverse operator 
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.
Received: 2011-10-14
Revised: 2012-03-12
Accepted: 2012-12-14
Published Online: 2013-10-08
Published in Print: 2013-12-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Ordinary and partial differential operators;
resolvent;
spectrum perturbations
Articles in the same Issue
- Masthead
- A characterization of pseudo-Einstein real hypersurfaces of a complex space form
- An application of Newton-type iterative method for the approximate implementation of Lavrentiev regularization
- Topological conjugation to uniformly piecewise linear transformations
- Strong convergence theorems for the approximation of fixed points of demicontinuous pseudocontractive mappings
- An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain
- Nondifferentiable (Φ,ρ)-type I and generalized (Φ,ρ)-type I functions in nonsmooth vector optimization
- An optimal double inequality between logarithmic and generalized logarithmic means
- A further generalization of the 𝒯𝒜d-density topology
- Erratum Bloch varieties of higher-dimensional, periodic Schrödinger operators [J. Appl. Anal. 15 (2009), 33–46]
