On Taylor coefficients of functions of classes $H_1$

  • V. V. Bovsunovska National technical University of Ukraine "KPI named after I. Sikorskyi", Kyiv
  • P. V.  Zaderey National technical University of Ukraine "KPI named after I. Sikorskyi", Kyiv
Keywords: coefficients

Abstract

UDC 517.5

We establish conditions imposed on the coefficients of a power series, under which the series under consideration is the Taylor series of a function belonging to the class $H_1$.

Author Biography

P. V.  Zaderey, National technical University of Ukraine "KPI named after I. Sikorskyi", Kyiv

 

 

References

I. I. Privalov, Granichnye svojstva analiticheskih funkcij, Gostekhizdat, Moskva, Leningrad (1950).

A. Zigmund, Тригонометрические ряды. Томы I, II. (Russian) [[Trigonometric series]] Izdat. ``Mir'', Moscow Vol. I: 615 pp.; Vol. II: 537 pp. (1965).

A. Kolmogoroff, Sur Lordre de grandeur des coefficients de la seria de Fourier – Lebesque, Bull. Acad. Polon., Ser. A, 83 – 86 (1923).

S. A. Telyakovskij, Nekotorye ocenki dlya trigonometricheskih ryadov s kvazivypuklymi koefficientami, Mat. sb., 63 (105), № 3, 426 – 444 (1964).

Published
17.06.2022
How to Cite
Bovsunovska , V. V., and P. V. Zaderey. “ On Taylor Coefficients of Functions of Classes $H_1$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 5, June 2022, pp. 725 -28, doi:10.37863/umzh.v74i5.7012.
Section
Short communications