منابع مشابه
On Matrix-valued Herglotz Functions
We 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 Nevanli...
متن کاملSome Applications of Operator-valued Herglotz Functions
We consider operator-valued Herglotz functions and their applications to self-adjoint perturbations of self-adjoint operators and self-adjoint extensions of densely defined closed symmetric operators. Our applications include model operators for both situations, linear fractional transformations for Herglotz operators, results on Friedrichs and Krein extensions, and realization theorems for cla...
متن کاملReflectionless Herglotz Functions and Generalized Lyapunov Exponents
We study several related aspects of reflectionless Jacobi matrices. Our first set of results deals with the singular part of reflectionless measures. We then introduce and discuss Lyapunov exponents, density of states measures, and other related quantities in a general setting. This is related to the previous material because the density of states measures are reflectionless on certain sets.
متن کاملA General Realization Theorem for Matrix-valued Herglotz-nevanlinna Functions
New special types of stationary conservative impedance and scattering systems, the so-called non-canonical systems, involving triplets of Hilbert spaces and projection operators, are considered. It is established that every matrix-valued Herglotz-Nevanlinna function of the form
متن کاملModeling Multipath Scattering Environments Using Generalized Herglotz Wave Functions
We develop a general mathematical model for nearfield multipath scattering as a basis for studying the spatial limits imposed on multi-antenna wireless communication systems. This model generalizes the Herglotz Wave Function, which is an important tool in the study of inverse scattering problems, to a form where the scatterers can be nearfield. This permits the development of the most general f...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2000
ISSN: 0025-584X,1522-2616
DOI: 10.1002/1522-2616(200010)218:1<61::aid-mana61>3.3.co;2-4