V. A. Strauss

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Articles: 4

Some class of real sequences having indefinite Hankel forms

Methods Funct. Anal. Topology 17 (2011), no. 1, 65-74

In this paper we generalize the results given in [14] about real sequences which are not necessarily positive (i.e, they are not sequences of power moments) but can be mapped, by a difference operator, into a power moment sequence. We prove by elementary methods that the integro-polynomial representation of such sequences remains after dropping the condition on its growth imposed in the mentioned article. Some additional results on the uniqueness of the representation are included.

On models of function type for a special class of normal operators in Krein spaces and their polar representation

Methods Funct. Anal. Topology 13 (2007), no. 1, 67-82

The paper is devoted to a function model representation of a normal operator $N$ acting in a Krein space. We assume that $N$ and its adjoint operator $N^{\#}$ have a common invariant subspace $L_{+}$ which is a maximal nonnegative subspace and has a representation as a sum of a finite-dimensional neutral subspace and a uniformly positive subspace. For $N$ we construct a model representation as the multiplication operator by a scalar function acting in a suitable function space. This representation is applied to the problem of existence of a polar representation for normal operators of $D_{\kappa}^+$-class.

On a spectral decomposition of a commutative operator family in spaces with indefinite metric

Methods Funct. Anal. Topology 11 (2005), no. 1, 10-20