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On zeros of holomorphic in a unit disk functions, determined by an arbitrary growth majorant
Sheparovych Iryna Bohdanivna 1
1 Department of Mathematics and Economics, Drohobych Ivan Franko state Pedagogical University, Lviv region, Drohobych, 82100, Ukraine
Keywords: unit disk, zeros sequence, holomorphic function, Fourier coefficients
Abstract
By a Fourier coefficients method we established necessary and sufficient conditions, under which the arbitrary sequence of complex numbers $(λ_v)$  is a sequence zeros for some classes of holomorphic in a unit disk functions, determined by an arbitrary growth majorant.
References

[1] Rubel, L.A., Taylor, B.A. (1968). A Fourier series method for meromorphic end entire functions: Bull.Soc. Math France, 96, 53 - 91.

[2] Kondratyuk, A.A. (1988). Fourier series and meromorphic functions. Lvov, U.: Higher school.

[3] Beck, W. (1970). Efficient quotient representations of meromorphic functions in the disc: Thesis. Urbana-Champaign, I: University of Illinois.

[4] Shamoyan, F. A. (1978). MM Dzhrbashyan factorization theorem and the characteristic of zeros of analytic functions with a majorant of finite growth: Izv. AN Arm. SSR Sir Mat., 13 (5-6), 405-422.

[5] Shamoyan, F. A. (1983). On zeros of analytic functions in a circle growing near the boundary: Izv. AN Arm. SSR Sir Mat., 18 (1), 15-27.

[6] Miles, J., Shea, D. (1976). On the growth of meromorphic functions having at least one definite value: Duke. Math J. 43, 171-186.

[7] Goldberg, AA, Ostrovsky, IV (1970) Distribution of values of meromorphic functions. Moscow, R .: Science.

[8] Tsuji, M. (1956). Canonical product of a meromorphic in a unit circle: J. Math. Soc Jap., 8 (1), 7-21.

[9] Naftalevich, A.A. (1961). On the interpolation of functions meromorphic in a unit circle: Lit. mat. Sat, 1 (1-2), 159 - 180.

[10] Dzhrbashyan M. (1948). On the canonical representation of meromorphic functions in a unit circle: Inform. Inst. mate. and the fur of the AN Arm. SSR Sir Mat., 2, 3 - 40.

[11] Hayman, U. (1980). Meromorphic functions. Moscow, R .: World.

Cite
ACS Style
Sheparovych, I.B. On zeros of holomorphic in a unit disk functions, determined by an arbitrary growth majorant. Bukovinian Mathematical Journal. 2018, 6 https://doi.org/ https://doi.org/10.31861/bmj2018.01.129
AMA Style
Sheparovych IB. On zeros of holomorphic in a unit disk functions, determined by an arbitrary growth majorant. Bukovinian Mathematical Journal. 2018; 6(1-2). https://doi.org/ https://doi.org/10.31861/bmj2018.01.129
Chicago/Turabian Style
Iryna Bohdanivna Sheparovych. 2018. "On zeros of holomorphic in a unit disk functions, determined by an arbitrary growth majorant". Bukovinian Mathematical Journal. 6 no. 1-2. https://doi.org/ https://doi.org/10.31861/bmj2018.01.129
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