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On the best approximation matrix problem and matrix Fourier series

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Approximation Theory and its Applications

Abstract

In this paper the concept of positive definite bilinear matrix moment functional, acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b] is introduced. The best approximation matrix problem with respect to such a functional is solved in terms of matrix Fourier series. Basic properties of matrix Fourier series such as the Riemann—Lebesgue, matrix property and the bessel—parseval matrix inequality are proved. The concept of total set with respect to a positive definite matrix functional is introduced, and the totallity of an orthonormal sequence of matrix polynomials with respect to the functional is established.

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Authors and Affiliations

  1. Department of Applied Mathematics, Polytechnical University of Valencia, P. O. Box 22, 012, Valencia, Spain

    L. Jódar, E. Navarro & E. Defez

Authors
  1. L. Jódar
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  2. E. Navarro
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  3. E. Defez
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Jódar, L., Navarro, E. & Defez, E. On the best approximation matrix problem and matrix Fourier series. Approx. Theory & its Appl. 13, 88–98 (1997). https://doi.org/10.1007/BF02836812

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  • DOI: https://doi.org/10.1007/BF02836812

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