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Uniqueness theorem for linear elliptic equation of the second order with constant coefficients

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Abstract

The interior uniqueness theorem for analytic functions was generalized by M. B. Balk to the case of polyanalytic functions of order n. He proved that if the zeros of a polyanalytic function have an accumulation point of order n, then this function is identically zero. In this paper the interior uniqueness theorem is generalized to the solution to a linear homogeneous second order differential equation of elliptic type with constant coefficients.

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Authors and Affiliations

  1. Kazan Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    I. A. Bikchantaev

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  1. I. A. Bikchantaev
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Correspondence to I. A. Bikchantaev.

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Original Russian Text © I.A. Bikchantaev, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 7, pp. 14–18.

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Bikchantaev, I.A. Uniqueness theorem for linear elliptic equation of the second order with constant coefficients. Russ Math. 61, 11–14 (2017). https://doi.org/10.3103/S1066369X17070027

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  • DOI: https://doi.org/10.3103/S1066369X17070027

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