首页|Resolvent and logarithmic residues of a singular operator pencil in Hilbert spaces
Resolvent and logarithmic residues of a singular operator pencil in Hilbert spaces
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
The present paper considers the operator pencil A(lambda) = A(0) + A(1)lambda, where A(0), A(1) &NOTEQUexpressionL; 0 are bounded linear mappings between complex Hilbert spaces and A0 is neither one-toone nor onto. Assuming that 0 is an isolated singularity of A(lambda) and that the image of A(0) is closed, certain operators are defined recursively starting from A(0) and A(1) and they are shown to provide a characterization of the image and null space of the operators in the principal part of the resolvent and of the logarithmic residues of A(lambda) at 0. The relations with the classical results based on ascent and descent in [10] are discussed. In the special case of A(0) being Fredholm of index 0, the present results characterize the rank of the operators in the principal part of the resolvent, the dimension of the subspaces that define the ascent and descent, the partial multiplicities, and the algebraic multiplicity of A(lambda) at 0. (c) 2022 Elsevier Inc. All rights reserved.
Local spectral propertiesChainsResolventFactorizationsLogarithmic residuesANALYTIC MATRIX FUNCTIONSASCENT DESCENT NULLITYGENERALIZED RESOLVENTFUNDAMENTAL EQUATIONSLINEAR-OPERATORSINVERSIONEIGENVALUESEXPANSIONSDEFECT
NSTL
Elsevier
