Titlebook: Contributions to Operator Theory in Spaces with an Indefinite Metric; The Heinz Langer Ann Aalt Dijksma,Israel Gohberg,Reinhard Mennicken B

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https://doi.org/10.1007/978-3-642-60725-7We prove that any bounded component of the numerical range of a matrix polynomial .(λ) contains at least one eigenvalue of .(λ). Moreover, the set of corresponding Jordan chains is complete.

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The Sympatric Origin of Phytophagous InsectsThe perturbation of the multiplication operator in the space ..(0,1) by a Volterra operator with degenerate kernel is a particular case of the socalled “Friedrichs model”. We characterize the point spectrum of such a perturbation and establish a sharp result on the Lyapunov stability in the case that the kernel vanishes on the diagonal.

Insatiable

D. Ebert,R. J. H. Payne,W. W. WeisserThe aim of the present paper is to compute the number of negative squares of certain functions, especially of some polynomials of several variables.

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,On the defect of noncontractive operators in Kre?n spaces: a new formula and some applications,We prove a formula for the defect of a noncontractive operator from one Krein space to another and give some applications of this notion to the study of the spectral properties of nondecreasing continuous or real analytic functions whose values are selfadjoint operators on a Hilbert space.

Bucket

,Positive differential operators in the Krein space L2(?n),We characterize a class of indefinite partial differential operators which are similar to selfadjoint operators in the Hilbert space ..(?.).

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An analysis of the block structure of ,,-inner functions,This paper is aimed at analyzing of the canonical block structure of ..-inner functions. Inspired by papers of Arov [1] and Dewilde/Dym [10], [11] a concept of parametrization of ..-inner functions is developed.

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