Download Characteristic Functions, Scattering Functions and Transfer by Daniel Alpay, Victor Vinnikov PDF

By Daniel Alpay, Victor Vinnikov

The notions of move functionality and attribute services proved to be primary within the final fifty years in operator concept and in procedure concept. Moshe Livsic performed a principal position in constructing those notions, and the publication encompasses a collection of rigorously selected refereed papers devoted to his reminiscence. subject matters comprise classical operator thought, ergodic concept and stochastic procedures, geometry of delicate mappings, mathematical physics, Schur research and approach thought. the diversity of themes attests good to the breadth of Moshe Livsic's mathematical imaginative and prescient and the deep influence of his work.

The ebook will entice researchers in arithmetic, electric engineering and physics.

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Math. , 32 (1977), 73–131. Sergey V. edu Eduard R. edu Operator Theory: Advances and Applications, Vol. 197, 51–76 c 2009 Birkh¨ auser Verlag Basel/Switzerland Bi-Isometries and Commutant Lifting Hari Bercovici, Ronald G. S. Livsic, one of the founders of modern operator theory Abstract. In a previous paper, the authors obtained a model for a bi-isometry, that is, a pair of commuting isometries on complex Hilbert space. -Nagy and the third author. One approach to describing the invariant subspaces for such a bi-isometry using this model is to consider isometric intertwining maps from another such model to the given one.

J. Staffans, “Conservative state-space realizations of dissipative system behaviors”, Integr. Equ. Oper. Theory, 54 (2006), no. 2, 151–213. [10] H. Bart, I. A. Kaashoek, Minimal Factorizations of Matrix and Operator Functions, Operator Theory: Advances and Applications, Vol. 1, Birkh¨auser, Basel, 1979. V. R. Tsekanovski˘ı, “Realization theorems for operator-valued Rfunctions”, Oper. Theory Adv. , 98 (1997), 55–91. V. R. Tsekanovski˘ı, “On classes of realizable operator-valued Rfunctions”, Oper.

15) (m∞ (λ) + μ) Im h . 16) WΘ (λ) = and VΘ (λ) = 4. Realization of inverse Stieltjes functions Let E be a finite-dimensional Hilbert space. The scalar versions of the definitions below can be found in [21]. We recall (see [14], [21]) that an operator-valued Herglotz-Nevanlinna function V (z) is Stieltjes if it is holomorphic in Ext[0, +∞) and Im [zV (z)] ≥ 0. 1. 1) t − z t 0 where α ≤ 0, β ≥ 0, and G(t) is a non-decreasing on [0, +∞) operator-valued function such that ∞ (dG(t)e, e) < ∞, ∀e ∈ E. V.

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