Abstract
It is known that any function in a Hilbert Bargmann–Fock space can be represented as the sum of a solution of a given homogeneous differential equation with constant coefficients and a function being a multiple of the characteristic function of this equation with conjugate coefficients. In the paper, a decomposition of the space of entire functions of one complex variable with the topology of uniform convergence on compact sets for the convolution operator is presented. As a corollary, a solution of the de la Vallée Poussin interpolation problem for the convolution operator with interpolation points at the zeros of the characteristic function with conjugate coefficient is obtained.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Fischer, J. Math. 148, 1 (1917).
V. Bargmann, Commun. Pure Appl. Math. 14, 187 (1961).
H. S. Shapiro, Bull. London Math. Soc. 21, 513 (1989).
J. Sebastian-i-Silva, in Mathematics: Collection of Translations of Foreign Articles (Inostrannaya Literatura, Moscow, 1957), Vol. 1, p. 60.
D. J. Newman and H. S. Shapiro, Bull. Am. Math. Soc. 72, 971 (1966).
V. V. Napalkov, Proc. Steklov Inst. Math. 235, 158 (2001).
H. Muggli, Comment. Math. Helv. 11, 151 (1938).
F. R. Gantmacher, The Theory of Matrices (Nauka, Moscow, 1966; Chelsea, New York, 1959).
V. V. Napalkov and A. A. Nuyatov, Sb. Math. 203 (2), 224 (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Napalkov, A.U. Mullabaeva, 2017, published in Doklady Akademii Nauk, 2017, Vol. 476, No. 3, pp. 269–271.
Rights and permissions
About this article
Cite this article
Napalkov, V.V., Mullabaeva, A.U. Fischer decomposition of the space of entire functions for the convolution operator. Dokl. Math. 96, 465–467 (2017). https://doi.org/10.1134/S1064562417050155
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562417050155