Abstract:
The classical balayages of measures and subharmonic functions are extended to a system of rays SS with common origin on the complex plane C. For an arbitrary subharmonic function v of finite order on C, this allows one to build a δ-subharmonic function on C that is harmonic outside of S, coincides with v on S outside of a polar set, and has the same growth order as v. Applications are given to the investigation of the relationship between the growth of an entire function on S and the distribution of its zeros. In the present second part of the project, the results and preliminaries of its first part are used essentially.
Citation:
B. N. Khabibullin, A. V. Shmeleva, Z. F. Abdullina, “Balayage of measures and subharmonic functions to a system of rays. II. Balayages of finite genus and growth regularity on a single ray”, Algebra i Analiz, 32:1 (2020), 208–243; St. Petersburg Math. J., 32:1 (2021), 155–181
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\paper Balayage of measures and subharmonic functions to a system of rays. II. Balayages of finite genus and growth regularity on a single ray
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 1
\pages 208--243
\mathnet{http://mi.mathnet.ru/aa1687}
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\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 1
\pages 155--181
\crossref{https://doi.org/10.1090/spmj/1642}
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This publication is cited in the following 5 articles:
B. N. Khabibullin, “Distributions of zeros and masses of entire and
subharmonic functions with restrictions on their growth along the strip”, Izv. Math., 88:1 (2024), 133–193
A. E. Salimova, “A version of the Malliavin–Rubel Theorem on entire functions of exponential type with zeros near the imaginary axis”, Russian Math. (Iz. VUZ), 66:8 (2022), 37–45
A. E. Salimova, B. N. Khabibullin, “Growth of entire functions of exponential type and characteristics of distributions of points along straight line in complex plane”, Ufa Math. J., 13:3 (2021), 113–125
A. E. Salimova, B. N. Khabibullin, “Growth of subharmonic functions along line and distribution of their Riesz measures”, Ufa Math. J., 12:2 (2020), 35–49
B.N. Khabibullin, “Integrals of subharmonic functions and their differences with weight over small sets on a ray”, Mat. Stud., 54:2 (2020), 162
Citation in format AMSBIB
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