Integral formulas of the type of Carleman and B. Ya.~Levin for meromorphic and subharmonic functions

E. B. Menshikova

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2022), pp. 37-53.

Résumé

When studying the relationships between the distributions of the zeros of holomorphic and entire functions with the addition of distributions of poles for meromorphic functions and the growth of these functions, it is important to relate these distributions with integral or other characteristics of growth. In a more general subharmonic framework, these are the relationships between the Riesz measure of a subharmonic function or the Riesz charge for the difference of such functions and the growth characteristics of such functions. The basis of such relationships, as a rule, is a variety of integral formulas. Often a complicating factor in the use of such formulas is the presence in them of derivatives from the functions under study. The article proposes an option to get rid of such difficulties by using inversion on the plane.

Détail

Keywords: meromorphic function, distribution of zeros and poles, $\delta$-subharmonic function, Riesz measure and charge, Carleman integral formula.

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