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Periodica Mathematica Hungarica

, Volume 22, Issue 3, pp 187–196 | Cite as

On some riesz bases

Article

Abstract

In this paper we consider three problems concerning systems of vector exponentials. In the first part we prove a conjecture of V. Komornik raised in [14] on the independence of the movement of a rectangular membrane in different points. It was independently proved by M. Horváth [9] and S. A. Avdonin (personal communication). The analogous problem for the circular membrane was partly solved in [3] — the complete solution is given in [10]. In the second part we fill in a gap in the theory of Blaschke-Potapov products developed in the paper [19] of Potapov. Namely we prove that the Blaschke-Potapov product is determined by its kernel sets up to a multiplicative constant matrix. In the third part of the present paper we give a multidimensional generalization of the notion of sine type function developed by Levin [16], [17] and by our generalization we prove the multidimensional variant of the Levin-Golovin basis theorem [16], [6].

Mathematics subject classification numbers, 1980/1985

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Copyright information

© Akadémiai Kiadó 1991

Authors and Affiliations

  • I. Joó
    • 1
  1. 1.Mathematical Institute of theHungarian Academy of SciencesBudapestHungary

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