By Jussi Behrndt, Karl-Heinz Förster, Heinz Langer, Carsten Trunk
This ebook incorporates a selection of contemporary examine papers originating from the sixth Workshop on Operator conception in Krein areas and Operator Polynomials, which was once held on the TU Berlin, Germany, December 14 to 17, 2006. The contributions during this quantity are dedicated to spectral and perturbation conception of linear operators in areas with an internal product, generalized Nevanlinna services and difficulties and purposes within the box of differential equations. one of the mentioned themes are linear family members, singular perturbations, de Branges areas, nonnegative matrices and summary kinetic equations.
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This publication incorporates a choice of contemporary examine papers originating from the sixth Workshop on Operator conception in Krein areas and Operator Polynomials, which used to be held on the TU Berlin, Germany, December 14 to 17, 2006. The contributions during this quantity are dedicated to spectral and perturbation thought of linear operators in areas with an internal product, generalized Nevanlinna capabilities and difficulties and functions within the box of differential equations.
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Additional resources for Spectral Theory in Inner Product Spaces and Applications: 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006
Example text
Lemma. Let E ∈ HB and d : R → N0 . (i) Let ω ∈ Admd (E). Then ω/ is minimal in Admd (E)/ if and only if ω/ is minimal in Adm(E)/ . (ii) The set Admd (E)/ contains at most one minimal element. Proof. 7]. 4]. We can now settle the question when, and in which way, finite-dimensional de Branges subspaces can be represented by majorants. Put R(E) := Rω (E) : ω ∈ Adm(E) . 8. Theorem. Let E ∈ HB and d : R → N0 . Then the following conditions are equivalent: (i) Admd (E)/ contains a minimal element; (ii) FSubd (E) ∩ R(E) = ∅; (iii) FSubd (E) = ∅ and Subd (E) ⊆ R(E).
Bognar, Indefinite Inner Product Spaces, Springer, 1974. [CL] B. Curgus and H. Langer, A Krein space approach to symmetric ordinary differential operators with an indefinite weight function, J. Differential Equations 79 (1989), 31–61. [DS] N. Dunford and J. Schwartz, Linear Operators Part I, General Theory, Interscience Publishers, 1958. Ya. Azizov, J. Behrndt, F. Philipp and C. Trunk P. Jonas and H. Langer, Compact perturbations of definitizable operators, J. Operator Theory 2 (1979), 63–77. G. K¨ othe, Topological Vector Spaces I, Springer, 1969.
Azizov, A. Dijksma, and H. Langer, The Schur algorithm for generalized Schur functions III: Factorizations of J-unitary matrix polynomials, Linear Algebra Appl. 369 (2003), 113–144. [3] D. Alpay, A. Dijksma, and H. Langer, J -unitary factorization and the Schur algorithm for Nevanlinna functions in an indefinite setting, Linear Algebra Appl. 419 (2006), 675–709. [4] D. Alpay, A. Dijksma, and H. Langer, The transformation of Issai Schur and related topics in an indefinite setting, Operator Theory: Adv.