scholarly journals Uniqueness of Entire Functions concerning Difference Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Chun Wu
Keyword(s):  
Difference Operator ◽  
Entire Functions ◽  
Difference Operators ◽  
Uniqueness Question

We deal with a uniqueness question of entire functions sharing a nonzero value with their difference operators and obtain some results, which improve the results of Qi et al. (2010) and Zhang (2011).

scholarly journals Uniqueness Problems about Entire Functions with Their Difference Operator Sharing Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Finite Order ◽  
Difference Operator ◽  
Entire Functions ◽  
Difference Operators ◽  
Transcendental Entire Functions

In this paper, we study the uniqueness questions of finite order transcendental entire functions and their difference operators sharing a set consisting of two distinct entire functions of finite smaller order. Our results in this paper improve the corresponding results from Liu (2009) and Li (2012).

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

Difference Operators in Simulation Data Warehouses

2017 ◽  
Vol 12 (2) ◽  
pp. 347-354 ◽  
Author(s):  
Jing Zhao ◽  
◽  
Yoshiharu Ishikawa ◽  
Yukiko Wakita ◽  
Kento Sugiura
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Observation Data ◽  
Temporal Data ◽  
Data Warehouses ◽  
Simulation Data ◽  
Tsunami Disaster ◽  
Spatio Temporal ◽  
The Difference ◽  
Mass Evacuation

In analyzing observation data and simulation results, there are frequent demands for comparing more than one data on the same subject to detect any differences between them. For example, comparison of observation data for an object in a certain spatial domain at different times or comparison of spatial simulation data with different parameters. Therefore, this paper proposes the difference operator in spatio-temporal data warehouses, which store temporal and spatial observation data and simulation data. The requirements for the difference operator are summarized, and the approaches to implement them are presented. In addition, the proposed approach is applied to the mass evacuation of simulation data in a tsunami disaster, and its effectiveness is verified. Extensions of the difference operator and their applications are also discussed.

scholarly journals Difference Equations and Sharing Values Concerning Entire Functions and Their Difference

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhiqiang Mao ◽  
Huifang Liu
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Value Distribution ◽  
Difference Operators ◽  
Sharing Values ◽  
Difference Analogue ◽  
The Difference ◽  
Brück Conjecture

The value distribution of solutions of certain difference equations is investigated. As its applications, we investigate the difference analogue of the Brück conjecture. We obtain some results on entire functions sharing a finite value with their difference operators. Examples are provided to show that our results are the best possible.

scholarly journals SPECTRAL PROPERTIES OF OPERATORS USING TRIDIAGONALIZATION

2012 ◽  
Vol 10 (03) ◽  
pp. 327-343 ◽  
Author(s):  
MOURAD E. H. ISMAIL ◽  
ERIK KOELINK
Keyword(s):  
Orthogonal Polynomials ◽  
Jacobi Polynomials ◽  
Difference Operator ◽  
General Scheme ◽  
Second Order ◽  
Order Differential Operator ◽  
Difference Operators ◽  
Jacobi Function ◽  
Wilson Polynomials ◽  
Tridiagonal Form

A general scheme for tridiagonalizing differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure of generally different orthogonal polynomials. Three examples are worked out: (1) related to Jacobi and Wilson polynomials for a second order differential operator, (2) related to little q-Jacobi polynomials and Askey–Wilson polynomials for a bounded second order q-difference operator, (3) related to little q-Jacobi polynomials for an unbounded second order q-difference operator. In case (1) a link with the Jacobi function transform is established, for which we give a q-analogue using example (2).

Entire functions sharing sets of small functions with their difference operators or shifts

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
BaoQin Chen ◽  
ZongXuan Chen
Keyword(s):  
Entire Functions ◽  
Difference Operators ◽  
Small Functions

AbstractWe show some interesting results concerning entire functions sharing two sets of small functions CM with their difference operators or shifts.

scholarly journals Estimates of Solutions of Elliptic Differential-Difference Equations with Degeneration

2018 ◽  
Vol 64 (1) ◽  
pp. 131-147
Author(s):  
V A Popov
Keyword(s):  
Difference Equations ◽  
A Priori Estimates ◽  
Difference Operator ◽  
A Priori ◽  
Difference Operators ◽  
Elliptic Differential Operator ◽  
Friedrichs Extension ◽  
Estimates Of Solutions ◽  
Priori Estimates ◽  
Differential Difference Equation

We consider a second-order differential-difference equation in a bounded domain Q ⊂ Rn. We assume that the differential-difference operator contains some difference operators with degeneration corresponding to differentiation operators. Moreover, the differential-difference operator under consideration cannot be expressed as a composition of a difference operator and a strongly elliptic differential operator. Degenerated difference operators do not allow us to obtain the G˚arding inequality. We prove a priori estimates from which it follows that the differential-difference operator under consideration is sectorial and its Friedrichs extension exists. These estimates can be applied to study the spectrum of the Friedrichs extension as well. It is well known that elliptic differential-difference equations may have solutions that do not belong even to the Sobolev space W 1(Q). However, using the obtained estimates, we can prove some smoothness of solutions, though not in the whole domain Q, but inside some subdomains Qr generated by the shifts of the boundary, where U Qr = Q.

scholarly journals Uniqueness of Functions with Its Shifts or Difference Operators

2018 ◽  
Author(s):  
Rajshree Dhar
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Difference Operator ◽  
Difference Operators

It is shown that if a non-constant meromorphic function f(z) is of finite order and shares certain values with its shifts/difference operators then f(z) coincides with that particular shift/difference operator.

Entire functions sharing some values with their difference operators

2014 ◽  
Vol 57 (10) ◽  
pp. 2143-2152 ◽  
Author(s):  
Jie Zhang ◽  
LiangWen Liao
Keyword(s):  
Entire Functions ◽  
Difference Operators
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