scholarly journals On deviations from rational functions of entire functions of finite lower order

2007 ◽  
Vol 91 (2-3) ◽  
pp. 161-177 ◽  
Author(s):  
E. Ciechanowicz ◽  
I. I. Marchenko
Keyword(s):  
Lower Order ◽  
Entire Functions ◽  
Rational Functions ◽  
Finite Lower Order

scholarly journals On transcendental directions of entire solutions of linear differential equations

2021 ◽  
Vol 7 (1) ◽  
pp. 276-287
Author(s):  
Zheng Wang ◽  
◽  
Zhi Gang Huang
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Lower Order ◽  
Difference Operator ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Entire Solutions ◽  
The Common ◽  
Linear Differential ◽  
Finite Lower Order

<abstract><p>This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 2) $ is an integer and $ A_i(z)(i = 0, 1, ..., n-1) $ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.</p></abstract>

Some growth properties of composite p-adic entire functions on the basis of their relative order and relative lower order

2019 ◽  
Vol 12 (03) ◽  
pp. 1950044
Author(s):  
Tanmay Biswas
Keyword(s):  
Growth Rates ◽  
Lower Order ◽  
Entire Functions ◽  
Closed Field ◽  
Relative Order ◽  
Algebraically Closed Field ◽  
Growth Properties

Let [Formula: see text] be a complete ultrametric algebraically closed field and [Formula: see text] be the [Formula: see text]-algebra of entire functions on [Formula: see text]. For [Formula: see text], [Formula: see text], we wish to introduce the notions of relative order and relative lower order of [Formula: see text] with respect to [Formula: see text]. Hence, after proving some basic results, in this paper, we estimate some growth rates of composite p-adic entire functions on the basis of their relative orders and relative lower orders.

scholarly journals A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Ruifang Zhao
Keyword(s):  
Sobolev Space ◽  
Unit Disk ◽  
Analytic Functions ◽  
Entire Functions ◽  
Rational Functions ◽  
Multiplication Operators ◽  
Disk Algebra ◽  
Strongly Irreducible ◽  
Similarity Invariant ◽  
Sobolev Disk Algebra

LetR(𝔻)be the algebra generated in Sobolev spaceW22(𝔻)by the rational functions with poles outside the unit disk𝔻¯. In this paper, we study the similarity invariant of the multiplication operatorsMginℒ(R(𝔻)), whengis univalent analytic on𝔻orMgis strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.

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