Blaschke products of given quantity index for a half-plane

Authors

  • Gagik Mikayelyan Yerevan State University
  • Feliks Hayrapetyan Institute of Mathematics, NAS RA

DOI:

https://doi.org/10.52737/18291163-2020.12.2-1-8

Keywords:

Blaschke Product, Integral Mean, Quantity Index

Abstract

We investigate the growth of the integral logarithmic means of Blaschke products for the half-plane. We prove the existence of Blaschke products of given quantity indices.

Author Biography

  • Gagik Mikayelyan, Yerevan State University

    PhD, YSU Associate Professor

References

Maclane G.R., Rubel L.A. On the growth of Blaschke product, Canadian J. of. Math., 21 (1969), no. 3, pp. 595-601. https://doi.org/10.4153/cjm-1969-067-3

Eiko V.V., Kondratyuk A.A. Integral logarithmic means of Blaschke products, Mat. Zametki, 64 (1998), no. 2, pp. 199-206. https://doi.org/10.1007/bf02310301

Sons L.R. Zeros of functions with slow growth in the unit disc, Math. Japonica, 24 (1979), no. 3, pp. 271-282.

G.V. Mikayelyan, Study of the growth of Blaschke-Nevanlinna type products by method of Fourier transforms method, Izv. AN Arm SSR, Ser. Matem., 18 (1983), no. 3, pp. 216-229.

A.M. Djrbashyan, Functions of Blaschke type for a half-plane, DAN SSSR, 246 (1979), no. 6, pp. 1295-1298.

G.V. Mikayelyan and F.V. Hayrapetyan, On integral logaritmic means of Blaschke products for a half-plane, Proceedings of the Yerevan state university, 52 (2018), no. 3, pp. 166-171. https://doi.org/10.46991/pysu:a/2018.52.3.166

M.O. Ghirnyk and A.A. Kondratyuk, Blaschke products of given quantity index, Math. Stud., 2 (1993), pp. 49-52.

R.S. Galoyan, On the asymptotic properties of a function $pi_p (z; z_k)$, DAN Arm SSR, 9 (1974), no. 2, pp. 65-71.

A.M. Djrbashyan and G.V. Mikayelyan, Asymptotic behavior of Blaschke like products for the half-plane, Izv. AN Arm SSR, Ser. Matem., 21 (1986), no. 2, pp. 142-162.

A.P. Prudnikov and Yu.A. Brychkov, Marichev O.I. Integrals and Series: Elementary functions, M. Nauka, 1981. https://doi.org/10.1201/9780203750643-2

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Published

2020-04-23 — Updated on 2022-08-29

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How to Cite

Blaschke products of given quantity index for a half-plane. (2022). Armenian Journal of Mathematics, 12(2), 1-8. https://doi.org/10.52737/18291163-2020.12.2-1-8 (Original work published 2020)