Non-self-adjoint operators, infinite determinants, and some applications
By Fritz Gesztesy, Yuri Latushkin, M. Mitrea, Maxim Zinchenko. 2005
51 citations recorded by the source corpus.
We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a variant of the Birman-Schwinger principle as well as local and global Weinstein-Aronszajn formulas. Our applications include a study of suitably symmetrized (modified) perturbation determinants of Schr\"odinger operators in dimensions n=1,2,3 and their connection with Krein's spectral shift function in two- and three-dimensional scattering theory. Moreover, we study an appropriate multi-dimensional analog of the celebrated formula by Jost and Pais that identifies Jost functions with suitable Fredholm (perturbation) determinants and hence reduces the latter to simple Wronski determinants.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/123f79d5c2d41c64500d90f17b6e2ed233e95c40
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Citations in the corpus
- Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, result): “The paper [35], in turn, was a continuation of the earlier papers [ 32 ] and [36], where we studied general, not necessarily self-adjoint, Schr¨ odinger operators on C 1,r -domains Ω ⊂ R n , n ∈ N, n 2, with compact boundaries ∂Ω, (1/2) 32 ] and [36].”
- Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, background): “The case of the Dirichlet Laplacian −�D, associated with formally corresponds to � = ∞ and so we isolate it in the next result (cf. also [ 22 ], [25]):”