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The Generalized Birman-Schwinger Principle
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The Generalized Birman-Schwinger Principle
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We prove a generalized Birman-Schwinger principle in the non-self-adjoint context. In particular, we provide a detailed discussion of geometric and algebraic multiplicities of eigenvalues of the basic operator of interest (e.g., a Schr\"odinger operator) and the associated Birman-Schwinger operator, and additionally offer a careful study of the associated Jordan chains of generalized eigenvectors of both operators. In the course of our analysis we also study algebraic and geometric multiplicities of zeros of strongly analytic operator-valued functions and the associated Jordan chains of generalized eigenvectors. We also relate algebraic multiplicities to the notion of the index of analytic operator-valued functions and derive a general Weinstein-Aronszajn formula for a pair of non-self-adjoint operators.
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Cited by 1 Pith paper
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Birman-Schwinger Formulation of the Faddeev-Popov Zero-Mode Problem
The first Gribov horizon of a transverse gauge background equals the first appearance of −1 in the spectrum of a normalized Birman-Schwinger operator, via an inertia-preserving congruence rather than a similarity.
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