Nevanlinna Theory of the Wilson Divided-difference Operator [PDF]
, 2017 Sitting at the top level of the Askey-scheme, Wilson polynomials are regarded as the most general hypergeometric orthogonal polynomials. Instead of a differential equation, they satisfy a second order Sturm-Liouville type difference equation in terms of ...
Cheng, Kam Hang, Chiang, Yik-Man
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Nevanlinna Theory for Jackson Difference Operators and Entire Solutions of q-Difference Equations [PDF]
Analysis Mathematica, 2021 This paper has two purposes. One is to establish a version of Nevanlinna theory based on the historic so-called Jackson difference operator Dqf(z)=f(qz)−f(z)qz−z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}
Tingbin Cao, H. X. Dai, Jing Wang
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Greatest common divisors of analytic functions and Nevanlinna theory on algebraic tori [PDF]
Journal für die Reine und Angewandte Mathematik, 2019 We study upper bounds for the counting function of common zeros of two meromorphic functions in various contexts. The proofs and results are inspired by recent work involving greatest common divisors in Diophantine approximation, to which we introduce ...
Aaron Levin, Julie Tzu‐Yueh Wang
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Ax–Schanuel type theorems on functional transcendence via Nevanlinna theory [PDF]
Mathematische Zeitschrift, 2021 In this paper, we apply Nevanlinna theory to prove two Ax–Schanuel type theorems for functional transcendence when the original exponential map is replaced by other meromorphic functions. We give examples to show that these results are optimal.
Jiaxing Huang, Tuen Wai Ng
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Nevanlinna theory for the difference operator [PDF]
, 2005 Certain estimates involving the derivative $f\mapsto f'$ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory.
Halburd, R. G., Korhonen, R. J.
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Nevanlinna analytic continuation for Migdal–Eliashberg theory [PDF]
Computational Materials TodayIn this work, we present a method to reconstruct real-frequency properties from analytically continued causal Green’s functions within the framework of Migdal–Eliashberg (ME) theory for superconductivity.
D.M. Khodachenko +4 more
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New results on the existences of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator and their applications [PDF]
Journal of Inequalities and Applications, 2017 In this paper, by using the Beurling-Nevanlinna type inequality we obtain new results on the existence of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator.
Xu Chen, Lei Zhang
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Studies of Differences from the point of view of Nevanlinna Theory [PDF]
Transactions of the American Mathematical Society, 2020 This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic function, holds. Second, a difference analogue of logarithmic derivative of
Jianhua Zheng, Risto Korhonen
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Difference Nevanlinna theories with vanishing and infinite periods [PDF]
, 2017 By extending the idea of a difference operator with a fixed step to varying-steps difference operators, we have established a difference Nevanlinna theory for meromorphic functions with the steps tending to zero (vanishing period) and a difference ...
Chiang, Yik-Man, Luo, Xudan
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Nevanlinna theory of the Askey-Wilson divided difference operator [PDF]
, 2018 This paper establishes a version of Nevanlinna theory based on Askey-Wilson divided difference operator for meromorphic functions of finite logarithmic order in the complex plane $\mathbb{C}$.
Chiang, Yik-Man, Feng, Shaoji
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