On the continuation of the Hartogs series with holomorphic coefficients

Authors

Takhir Tuychiev, National University of UzbekistanFollow
Jurabay Tishabaev, National University of UzbekistanFollow

Abstract

In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.

First Page

69

Last Page

76

References

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Recommended Citation

Tuychiev, Takhir and Tishabaev, Jurabay (2019) "On the continuation of the Hartogs series with holomorphic coefficients," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 2: Iss. 1, Article 5.
DOI: https://doi.org/10.56017/2181-1318.1021