Overdetermined interpolation problems for entire functions of the exponential type

1Volchkov, VV, 1Volchkov, Vit.V
1Vasyl Stus Donetsk National University
Dopov. Nac. akad. nauk Ukr. 2014, 6:13-16
Section: Mathematics
Language: Russian

Criteria for the existence of entire functions of the exponential type of at most ς which take the given values at the points from the given sequence of numbers with a density of more than ς are obtained.

Keywords: exponential type, functions, interpolation problems

1. Golberg A. A., Levin B. Ya., Ostrovsky I. V. Entire and meromorphic functions. In: The results of science and technology. Modern problems of mathematics. Fundamental directions. Vol. 85. Moscow: VINITI, 1991: 5–185 (in Russian).
2. Gelfond A. O. Calculus of finite differences.Moscow: Nauka, 1967 (in Russian).
3. Khermander L. Introduction to the theory of functions of several complex variables. Moscow: Mir, 1968 (in Russian).
4. Markushevich A. I. Selected chapters of the theory of analytic functions. Moscow: Nauka, 1976 (in Russian).
5. Biberbakh L. Analytical continuation. Moscow: Nauka, 1967 (in Russian).
6. Volchkov V. V., Volchkov Vit. V. Offbeat integral geometry on symmetric spaces. Heidelberg: Springer, 2013. https://doi.org/10.1007/978-3-0348-0572-8
7. Helgason S. Groups and geometric analysis. Moscow: Mir, 1987 (in Russian).
8. Volchkov V. V., Volchkov Vit. V. Harmonic analysis of mean periodic functions on symmetric spaces and the Heisenberg group. London: Springer, 2009. https://doi.org/10.1007/978-1-84882-533-8
9. Volchkov V. V. Integral geometry and convolution equations. Dordrecht: Kluwer, 2003. https://doi.org/10.1007/978-94-010-0023-9