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Orthonormal polynomial bases in function spaces

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Abstract

We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.

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References

  1. S. V. Bočkariov,Construction using Fejer kernels of interpolating dyadic basis in the space of continuous functions, Trudy Steklov Inst.172 (1985), 29–59 (in Russian).

    Google Scholar 

  2. S. V. Bočkariov,Construction of polynomial bases in finite dimensional spaces of functions analytic in the unit disc, Trudy Steklov Inst.164 (1983), 49–74 (in Russian).

    Google Scholar 

  3. S. V. Bočkariov,Conjugate Franklin system — a basis in the space of continuous functions, Dokl. Akad. Nauk285 (1985), 521–526 (in Russian).

    Google Scholar 

  4. J. Bourgain,Homogeneous polynomials on the ball and polynomial bases, Isr. J. Math.68 (1989), 327–347.

    Article  MATH  MathSciNet  Google Scholar 

  5. Z. A. Čanturija,On orthogonal polynomial bases in the spaces C and L, Analysis Math5 (1) (1979), 9–17.

    Article  Google Scholar 

  6. Z. A. Chanturia,On unconditional polynomial bases of the space L p , Studia Math.71 (1981), 163–168.

    MATH  MathSciNet  Google Scholar 

  7. R. R. Coifman and G. Weiss,Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc.83 (1977), 569–645.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Faber,Über die interpolatorische Darstelung stetige Funktionen, Jahresber. D. M. V.23 (1914), 192–210.

    Google Scholar 

  9. C. Foias and I. Singer,Some remarks on strongly linearly independent sequences and bases in Banach spaces, Revue Rom. Math. Pures Appl.16(3) (1961), 589–594.

    MathSciNet  Google Scholar 

  10. P. P. Korovkin,Linear operators and approximation theory, Fiz.-Mat. Gos. Izdat., Moscow (1959) (in Russian).

    Google Scholar 

  11. M.I. Kadec and A. Pełczyński,Bases, lacunary sequences and complemented subspaces in the spaces L p , Studia Math.21 (1962), 161–176.

    MATH  MathSciNet  Google Scholar 

  12. Al. A. Privalov,On the growth of degrees of polynomial basis and approximation of trigonometric projections, Mat. Zametki42(2) (1987), 207–214 (in Russian).

    MATH  MathSciNet  Google Scholar 

  13. Al. A. Privalov,On the growth of degrees of polynomial bases, Mat. Zametki48(4) (1990), 69–78 (in Russian).

    MathSciNet  Google Scholar 

  14. B. Shekhtman,On the norms of interpolating operators, Israel J. Math.64(1) (1989), 39–48.

    Article  MathSciNet  Google Scholar 

  15. B. Shekhtman,On polynomial “interpolation” in L 1 , preprint.

  16. E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.

  17. A. Torchinsky,Real-Variable Methods in Harmonic Analysis, Academic Press, New York, 1986.

    MATH  Google Scholar 

  18. P. L. Ulianov,On some solved and unsolved problems in the theory of orthogonal series, Proc. IV All Union Math. Congress2, Publishing House AN SSSR, Moscow (1964), 694–704 (in Russian).

    Google Scholar 

  19. P. L. Ulianov,On some results and problems in the theory of bases, Zapiski LOMI, 274–283 (in Russian).

  20. P. Wojtaszczyk,The Franklin system is an unconditional basis in H 1 , Arkiv für Mathematik20(2) (1982), 293–300.

    Article  MATH  MathSciNet  Google Scholar 

  21. P. Wojtaszczyk,Banach Spaces for Analysts, Cambridge University Press (to appear).

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Wojtaszczyk, P., Woźniakowski, K. Orthonormal polynomial bases in function spaces. Israel J. Math. 75, 167–191 (1991). https://doi.org/10.1007/BF02776023

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  • DOI: https://doi.org/10.1007/BF02776023

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