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Статья
2016

Summary equation for functions analytical outside a quadrangle


F. N. Garif’yanovF. N. Garif’yanov
Русская математика
https://doi.org/10.3103/S1066369X16100017
Abstract / Full Text

We consider a linear four-element functional equation. Its solutions are holomorphic outside of a quadrangle and vanish at the infinity point. This equation generates a system of entire functions of completely regular growth, which is bi-orthogonal on three rays with piecewise exponential weight to the system of powers.

Author information
  • Kazan State Power Engineering University, ul. Krasnosel’skaya 51, Kazan, 420066, RussiaF. N. Garif’yanov
References
  1. Garif’yanov, F. N., Modina, S. A. “On the Four-Element Equation for the Functions Analytic Beyond a Trapezoid and its Applications”, Sib. Math. J. 52, No. 2, 191–196 (2011).
  2. Zverovich, Eh. I. “AMethod of Locally Conformal Gluing”, Sov.Math.Dokl. 13, 1003–1007 (1972).
  3. Aksent’eva, E. P., Garif’yanov, F. N. “On the Analysis of an Integral Equation with Carleman Kernel”, Soviet Mathematics (Iz. VUZ) 27, No. 4, 53–63 (1983).
  4. Bieberbach, L. Analytische Fortsetzung (Springer-Verlag, Berlin–Göttingen–Heidelberg, 1955; Nauka, Moscow, 1967).
  5. Levin, B. Ya. The Distribution of the Zeroes of Entire Functions (Nauka, Moscow, 1956) [in Russian].
  6. Leont’ev, A. F. Exponential Series (Nauka, Moscow, 1976) [in Russian].
  7. Garif’yanov, F. N. “The Moment Problem for Entire Functions of Exponential Type”, Russian Mathemarics (Iz. VUZ) 47, No. 6, 33–39 (2003).