Results 1 to 10 of about 575,732 (183)
Manifolds of difference polynomials [PDF]
Transactions of the American Mathematical Society, 1948 1. It is the purpose of this paper to develop in some detail the structure of the manifolds determined by systems of difference polynomials. Our results will necessarily be confined to the case of polynomials in an abstract field, since a suitable existence theorem for analytic difference equations is not available. The ideal theory, developed by J. F.
Richard M. Cohn
openalex +3 more sources
Uniqueness of difference polynomials
AIMS Mathematics, 2021 Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)
Xiaomei Zhang , Xiang Chen
doaj +3 more sources
An existence theorem for difference polynomials [PDF]
Proceedings of the American Mathematical Society, 1966 Introduction. The abstract varieties (also called manifolds) of difference algebra [2], [3] have not heretofore had a realization as sets of functions comparable to the realization provided for differential manifolds by the analytic existence theorem for differential equations (see [4], particularly p. 23).
Richard M. Cohn
openalex +3 more sources
Value Distributions and Uniqueness of Difference Polynomials [PDF]
Advances in Difference Equations, 2011 We investigate the zeros distributions of difference polynomials of meromorphic functions, which can be viewed as the Hayman conjecture as introduced by (Hayman 1967) for difference.
Liu Kai, Liu Xinling, Cao TingBin
doaj +4 more sources
Skew Divided Difference Operators and Schubert Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group.
Anatol N. Kirillov
doaj +2 more sources
On the Deficiencies of Some Differential-Difference Polynomials [PDF]
Abstract and Applied Analysis, 2014 The characteristic functions of differential-difference polynomials are investigated, and the result can be viewed as a differential-difference analogue of the classic Valiron-Mokhon’ko Theorem in some sense and applied to investigate the deficiencies of
Xiu-Min Zheng, Hong Yan Xu
doaj +4 more sources
On a difference equation for generalizations of Charlier polynomials
Journal of Approximation Theory, 1999 11 ...
H. Bavinck, Roelof Koekoek
openalex +5 more sources
Difference sets and Polynomials of prime variables [PDF]
Acta Arithmetica, 2007 Let (x) be a polynomial with rational coefficients. Suppose that has the positive leading coefficient and zero constant term. Let A be a set of positive integers with the positive upper density. Then there exist x,y\in A and a prime p such that x-y= (p-1).
Hongze Li, Hao Pan
openalex +5 more sources
The Zeros of Difference Polynomials of Meromorphic Functions
Abstract and Applied Analysis, 2012 We investigate the value distributions of difference polynomials Δf(z)-af(z)n and f(z)nf(z+c) which related to two well-known differential polynomials, where f(z) is a meromorphic function.
Junfeng Xu, Xiaobin Zhang
doaj +4 more sources
On the generalized difference polynomials [PDF]
Pacific Journal of Mathematics, 1990 Laurenţiu Panaitopol, D. M. Stefanescu
openalex +3 more sources