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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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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Ax-Schanuel Type Theorems on Functional Transcendence via Nevanlinna\n Theory [PDF]
Mathematische Zeitschrift, 2019 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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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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Nevanlinna theory of the Wilson divided-difference operator [PDF]
, 2017 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 $\mathbb{C}$.
Kam Hang Cheng, Yik‐Man Chiang
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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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Nevanlinna theory via holomorphic forms [PDF]
Pacific Journal of Mathematics, 2022 . This paper re-develops Nevanlinna theory for meromorphic functions on C in the viewpoint of holomorphic forms. According to our observation, Nevanlinna’s functions can be formulated by a holomorphic form.
Xianjing Dong, Shuangshuang Yang
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Finite and infinite order of growth of solutions to linear differential equations near a singular point [PDF]
Mathematica Bohemica, 2021 In this paper, we investigate the growth of solutions of a certain class of linear differential equation where the coefficients are analytic functions in the closed complex plane except at a finite singular point.
Samir Cherief, Saada Hamouda
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On Some New Results in Large Area Nevanlinna Spaces in the Unit Disk
Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2023 The study of various infinite products in various spaces of analytic functions in the unit disk is a well known and well studied problem of complex function theory in the unit disk.
Shamoyan, R., Mihi´c, O.
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