Representation of analytic functions by series of exponentials on a half-plane with a given estimate of entire component

Галия Гайсина
2021 International scientific conference "Ufa autumn mathematical school - 2021"   unpublished
Èçó÷àåòñÿ çàäà÷à î ïðåäñòàâëåíèè àíàëèòè÷åñêèõ â ïîëóïëîñêîE ñòè ôóíêöèé ðÿäàìè ýêñïîíåíò ñ ó÷åòîì çàäàííîé âûïóêëîé ìàE aeîðàíòû ðîñòàD íå îãðàíè÷åííîé â îêðåñòíîñòè íóëÿF Ìåòîäû îöåE íîê îñíîâàíû íà ñâîéñòâàõ ïðåîáðàçîâàíèé ËåaeàíäðàF Êëþ÷åâûå ñëîâàX ðÿäû ýêñïîíåíòD öåëàÿ ôóíêöèÿD âûïóêëàÿ ìàE aeîðàíòà Representation of analytic functions by series of exponentials on a half-plane with a given estimate of entire component We study the problem of representing analytic in a half-plane functions
more » ... y exponential series taking into account a given convex majorant of growth that is not bounded in a neighborhood of zero. The estimation methods are based on the properties of the Legendre transformations.
doi:10.33184/mnkuomsh1t-2021-10-06.42 fatcat:3tbtzcy2jfgcfa3kis2okhjzqy