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Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K)

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Abstract

For any ε > 0, we construct an orthonormal Schauder basis of C(K) consisting of trigonometric polynomials Tn n = 1, 2, . . . , such that deg(Tn) ≤ (1/2)(1 + ε)n. This is best possible with regard to the degree. The construction uses wavelet techniques.

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Authors and Affiliations

  1. Gesellschaft f¨ur Mathematik und Datenverarbeitung, Sankt Augustin, Germany

    R.A. Lorentz

  2. Mathematical Institute, Armenian Academy of Sciences, Yerevan, Armenia

    A.A. Sahakian

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  1. R.A. Lorentz
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  2. A.A. Sahakian
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Lorentz, R., Sahakian, A. Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K). J Fourier Anal Appl 1, 103–112 (1994). https://doi.org/10.1007/s00041-001-4005-8

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  • DOI: https://doi.org/10.1007/s00041-001-4005-8

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