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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.

Some approximation problems in $L^{p}$ -spaces of matrix-valued functions

Lutz Klotz — 1991

Studia Mathematica

An interpolation problem for multivariate stationary sequences

Lutz Klotz — 2000

Kybernetika

Let $𝐗$ and $𝐘$ be stationarily cross-correlated multivariate stationary sequences. Assume that all values of $𝐘$ and all but one values of $𝐗$ are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

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Currently displaying 1 – 3 of 3

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

Some approximation problems in L p -spaces of matrix-valued functions

An interpolation problem for multivariate stationary sequences

Some approximation problems in $L^{p}$ -spaces of matrix-valued functions