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 کاملSemismooth Matrix-Valued Functions
Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, -derivative, directional derivative, and sem...
متن کاملOn differentiability of symmetric matrix valued functions
With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of the corr...
متن کاملOn Periodic Matrix-Valued Weyl-Titchmarsh Functions
We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh matrixvalued functions as well as a new version of the functional model in such realizations are presented. In the case of periodic Herglotz-Nevanlinna matrix-v...
متن کاملA Study on Nonsymmetric Matrix-valued Functions
2009 Acknowledgements I would like to express my sincere gratitude to my supervisor, Professor Sun Defeng for all of his guidance, encouragement and support. He taught me how to do research and did it with great care and patience. his patient guidance and great help. I would also like to acknowledge National University of Singapore for providing me the financial support and the pleasant environ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1978
ISSN: 0024-3795
DOI: 10.1016/0024-3795(78)90053-8