Limiting absorption principle and singular spectrum
Nurulla Azamov
TL;DR
This paper introduces an explicit construction of eigenspaces for points in the singular spectrum of self-adjoint operators, using an abstract homogeneous Lippmann-Schwinger equation, advancing spectral analysis techniques.
Contribution
It provides a novel explicit construction method for eigenspaces associated with the singular spectrum of self-adjoint operators.
Findings
Constructed an analogue of eigenspaces for singular spectrum points.
Utilized an abstract homogeneous Lippmann-Schwinger equation.
Enhanced understanding of spectral properties of self-adjoint operators.
Abstract
In this paper I give an explicit construction of an analogue of eigenspace for points of the singular spectrum of a self-adjoint operator. This construction is based on an abstract version of homogeneous Lippmann-Schwinger equation.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum chaos and dynamical systems · Quantum optics and atomic interactions