Variation of Subharmonic Function under Transformation of its Riesz Measure


  • E. G. Kudasheva Chair of Mathematics, Bashkir State Agrarian University, 34, 50 Let Oktyabrya Str., Ufa, 450001, Bashkortostan, Russia
  • B. N. Khabibullin Department of Mathematics, Bashkir State University, 32 Frunze Str., Ufa, 450074, Russia
    Institute of Mathematics with Computing Centre, Ural Branch of the USSR Academy of Sciences, 112 Chernyshevskii Str., Ufa, 450077, Russia


The paper combines two aspects. First, it contains a compressed comparative review of the well-known results on the change of growth of entire (subharmonic resp.) function under the shifts of its zeros (under T-shift of its Riesz measure resp.). There was B.Ya. Levin who stood at the sources of these results. Second, the first coauthor proves new results obtained in this direction: the estimates of change of subharmonic function under integral restrictions for T-shift of its Riesz measure, and also, in a certain sense, an optimal approximation of an entire function by the entire function with simple zeros.*

Mathematics Subject Classification: 30D15, 31A05.

Ключові слова:

entire function, subharmonic function, shift of zeros, Riesz measure, T-shift of measure.


Як цитувати

Kudasheva, E. G.; Khabibullin, B. N. Variation of Subharmonic Function under Transformation of its Riesz Measure. Журн. мат. фіз. анал. геом. 2007, 3, 61-94.





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