Seminars: K. Kh. Rakhimov, Sh. Sh. Shopulatov, An integral criterion for $m-sh$-functions

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) April 22, 2021 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

An integral criterion for $m-sh$-functions K. Kh. Rakhimov^ab, Sh. Sh. Shopulatov^c ^a Centre National de la Recherche Scientifique, Paris ^b Université de Lille ^c V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan
Abstract: It is well-known that subharmonic functions are defined by integral mean value, i.e. mean value over the sphere (ball) of the function at the neighbourhood of the point is greater or equal to the value of the function at this point. Plurisubharmonic and $m$-subharmonic functions are defined by using subharmonicity at complex lines and $m$-dimensional complex planes, respectively. In this talk we introduce a new integral criterion for $m-sh$-functions. It can be used like subharmonic functions as a definition for $m-sh$-functions. In particular the obtained results can be applied for plurisubharmonic functions. Website: https://us02web.zoom.us/j/8022228888