On Matrix-Valued Herglotz Functions

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dc.creatorGesztesy, Fritz
dc.creatorTsekanovskii, Eduard
dc.date1997-12-11
dc.date.accessioned2026-07-07T03:24:40Z
dc.date.available2026-07-07T03:24:40Z
dc.descriptionWe provide a comprehensive analysis of matrix-valued Herglotz functions and illustrate their applications in the spectral theory of self-adjoint Hamiltonian systems including matrix-valued Schrödinger and Dirac-type operators. Special emphasis is devoted to appropriate matrix-valued extensions of the well-known Aronszajn-Donoghue theory concerning support properties of measures in their Nevanlinna-Riesz-Herglotz representation. In particular, we study a class of linear fractional transformations M_A(z) of a given n \times n Herglotz matrix M(z) and prove that the minimal support of the absolutely continuos part of the measure associated to M_A(z) is invariant under these linear fractional transformations. Additional applications discussed in detail include self-adjoint finite-rank perturbations of self-adjoint operators, self-adjoint extensions of densely defined symmetric linear operators (especially, Friedrichs and Krein extensions), model operators for these two cases, and associated realization theorems for certain classes of Herglotz matrices.
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dc.identifierhttps://arxiv.org/abs/funct-an/9712004
dc.identifierhttp://arxiv.org/abs/funct-an/9712004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/33418
dc.subjectFunctional Analysis
dc.subjectMathematical Physics
dc.subject30D50, 30E20, 47A10 (primary) 47A45 (secondary)
dc.titleOn Matrix-Valued Herglotz Functions
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