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

Part of the Contemporary Mathematicians book series (CM)


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


Stationary Gaussian Noise Weighted Hardy Minimal Exponential Type Bernstein Problem Smallest Borel Field 
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  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

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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