2015/10/09 by Yik‐Man Chiang, Yik-Man Chiang, Xu‐Dan Luo +3
Mathematics · Medicine · #30D15 #30D35 #39A05 #39A70 #Complex Variables (math.CV) #Endometriosis Research and Treatment #FOS: Mathematics #Meromorphic and Entire Functions #math.CV #msc:30D15 #msc:30D35 #msc:39A05 #msc:39A70
paper · pdf · doi:10.48550/arxiv.1510.02576
27 pages, 1 figure. Some minor changes. To appear in Michigan Mathematical Journal
openalex publication_date 2015/10/09 · arxiv created 2017/03/13 · arxiv updated 2017/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Nevanlinna theory for finite order meromorphic functions with the steps tending to infinity (infinite period) in this paper. We can recover the classical little Picard theorem from the vanishing period theory, but we require additional finite order growth restriction for meromorphic functions from the infinite period theory. Then we give some applications of our theories to exhibit connections between discrete equations and and their continuous analogues.