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Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

Klotz, Lutz, Zagorodnyuk, Sergey M. (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. We find conditions for density of polynomials in this space using a connection with the L^2 space of square-integrable matrix-valued functions on R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.

Derivative and antiderivative operators and the size of complex domains

Luis Bernal-González (1994)

Annales Polonici Mathematici

We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.

Disjoint hypercyclic operators

Luis Bernal-González (2007)

Studia Mathematica

We introduce the concept of disjoint hypercyclic operators. These are operators performing the approximation of any given vectors with a common subsequence of iterates applied on a common vector. The notion is extended to sequences of operators, and applied to composition operators and differential operators on spaces of analytic functions.

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