Abstract
f ∗(γ) (\(\gamma = a + ib\)) denotes the regular extension of \(f^{{\ast}}(a) = f(a)^{{\ast}}\) so that \(f^{{\ast}}(\gamma ) = (f(\gamma ^{{\ast}}))^{{\ast}}\), (\(\gamma ^{{\ast}} = a - ib\)).
Supported in part by the Office of Naval Research and in part by the National Science Foundation, GP-149. Massachusetts Institute of Technology.
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References
A. Beurling. On two problems concerning linear transformations in Hilbert space. Acta Math., 81:239–255, 1949.
R. P. Boas. Entire functions. Academic Press, New York, 1954.
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.
Y. Domar. Closed primary ideals in a class of Banach algebras. Math. Scand., 7:109–125, 1959.
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.
T. Hida. Canonical representations of Gaussian processes and their applications. Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math., 33:109–155, 1960.
K. Hoffman. Banach Spaces of Analytic Functions. Prentice-Hall Series in Modern Analysis. Prentice-Hall Inc., New Jersey, 1962.
N. Levinson. Gap and Density Theorems. Number 26 in American Mathematical Society Colloquium Publications. American Mathematical Society, New York, 1940.
H. P. McKean. Brownian motion with a several-dimensional time. Teor. Verojatnost. i Primenen., 8:357–378, 1963.
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.
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”.
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Levinson, N., McKean, H.P. (2015). Weighted Trigonometrical Approximation on ℝ1 with Application to the Germ Field of a Stationary Gaussian Noise. In: Grünbaum, F., van Moerbeke, P., Moll, V. (eds) Henry P. McKean Jr. Selecta. Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-22237-0_13
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