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Weighted Trigonometrical Approximation on ℝ1 with Application to the Germ Field of a Stationary Gaussian Noise

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Part of the Contemporary Mathematicians book series (CM)

Abstract

f(γ) (\(\gamma = a + ib\)) denotes the regular extension of \(f^{{\ast}}(a) = f(a)^{{\ast}}\) so that \(f^{{\ast}}(\gamma ) = (f(\gamma ^{{\ast}}))^{{\ast}}\), (\(\gamma ^{{\ast}} = a - ib\)).

Keywords

Stationary Gaussian Noise Weighted Hardy Minimal Exponential Type Bernstein Problem Smallest Borel Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    A. Beurling. On two problems concerning linear transformations in Hilbert space. Acta Math., 81:239–255, 1949.CrossRefzbMATHGoogle Scholar
  2. [2]
    R. P. Boas. Entire functions. Academic Press, New York, 1954.zbMATHGoogle Scholar
  3. [3]
    T. Carleman. L’Intégrale de Fourier et Questions que s’y Rattachent, volume 1 of Publications Scientifiques de l’Institut Mittag-Leffler. Almqvist & Wiksells, Uppsala, 1944.Google Scholar
  4. [4]
    Y. Domar. Closed primary ideals in a class of Banach algebras. Math. Scand., 7:109–125, 1959.MathSciNetzbMATHGoogle Scholar
  5. [5]
    I. O. Hačatrjan. Weighted approximation of entire functions of zero degree by polynomials on the real axis. Dokl. Akad. Nauk SSSR, 145:744–747, 1962.MathSciNetGoogle Scholar
  6. [6]
    T. Hida. Canonical representations of Gaussian processes and their applications. Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math., 33:109–155, 1960.MathSciNetzbMATHGoogle Scholar
  7. [7]
    K. Hoffman. Banach Spaces of Analytic Functions. Prentice-Hall Series in Modern Analysis. Prentice-Hall Inc., New Jersey, 1962.zbMATHGoogle Scholar
  8. [8]
    N. Levinson. Gap and Density Theorems. Number 26 in American Mathematical Society Colloquium Publications. American Mathematical Society, New York, 1940.Google Scholar
  9. [9]
    H. P. McKean. Brownian motion with a several-dimensional time. Teor. Verojatnost. i Primenen., 8:357–378, 1963.MathSciNetGoogle Scholar
  10. [10]
    S. N. Mergelyan. Weighted approximations by polynomials. Uspehi Mat. Nauk (N.S.), 11:107–152, 1956. Amer. Math. Soc. Transl. Ser. 2, 10:59–106, 1958.Google Scholar
  11. [11]
    V. N. Tutubalin and M. I. Freĭdlin. On the structure of the infinitesimal \(\sigma\)-algebra of a Gaussian process. Teor. Verojatnost. i Primenen., 7:204–208, 1962. Translation in “Theor. Probab. Appl. 7:196–199, 1962”.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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