Some approximation problems in -spaces of matrix-valued functions
An interpolation problem for multivariate stationary sequences
Let and be stationarily cross-correlated multivariate stationary sequences. Assume that all values of and all but one values of 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].
Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
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.
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