Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
6.04.1994
Phone: +7 (963) 903-96-66
Keywords: Subharmonic function, entire function of exponential type, distribution of zeros,
completeness of systems of functions,
sweeping,
convex set,
logarithmic characteristics and measures,
growth of the entire function,
Lindelof condition,
complex sequence,
Riesz measure,
convolution,
imaginary axis
UDC: 517.574, 517.537, 517.518, 517.547.22, 517.982.47, 517.44, 517.538.2, 517.547.2 MSC: 31A05, 30D20, 30D15
Subject:
Distribution of zeros of a subharmonic function. The results are formulated in terms of special "logarithmic" characteristics of the measures vu and µM, which appeared earlier in the classical works of P. Malliavin, L. A. Rubel, etc.for sequences of points, as well as in terms of special "logarithmic" characteristics of the behavior of the function M along the imaginary axis and the function q along the real axis. The results obtained are also new for the distribution of the roots of exponential entire functions under restrictions on the growth of such functions along a straight line. The latter is illustrated by a new uniqueness theorem for integer functions of exponential type, using the so-called logarithmic block densities of the distribution of points on the complex plane.
Main publications:
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, “Distribution of Zeros of Exponential-Type Entire Functions with Constraints on Growth along a Line”, Math. Notes, 108:4 (2020), 579–589
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
