Open AccessREMARKS ON SOME CLASSES OF POSITIVE CONTINUOUS FUNCTIONS IN C^n
Author(s) -
Andriy Bandura
Publication year - 2021
Publication title -
prikarpatsʹkij vìsnik ntš. čislo
Language(s) - English
Resource type - Journals
ISSN - 2304-7399
DOI - 10.31471/2304-7399-2020-1(59)-9-15
Subject(s) - bounded function , mathematics , uniform boundedness , logarithm , class (philosophy) , function (biology) , logarithmic derivative , pure mathematics , derivative (finance) , index (typography) , vector valued function , zero (linguistics) , discrete mathematics , combinatorics , mathematical analysis , computer science , financial economics , economics , linguistics , philosophy , artificial intelligence , evolutionary biology , world wide web , biology
Here we prove two propositions providing sufficient conditions of belonging positive continuous functions in to classes and These auxiliary classes plays important role in theory of entire functions of bounded L-index in direction and bounded L-index in joint variables, where are continuous functions. They help to constuct general theory of bounded index for very wide class of entire functions, because for every entire functions with bounded multiplicities of zero points there exists a corresponding function or providing boundedness of L-index in direction or boundedness L–index in joint variables respectively. Our result requires uniform boundedness of logarithmic derivative in all variables and for belonging the function to class Q^n. Another result requires uniform boundedness of logarithmic derivative in directions and for belonging the function to class Q^n_b where is the complex conjugate vector to b.