(p,q) th order oriented growth measurement of composite p -adic entire functions
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 2
Abstract
Let us consider K be a complete ultrametric algebraically closed field and suppose A(K) be the K-algebra of entire functions on K. For any p-adic entire functions f∈A(K) and r>0, we denote by |f|(r) the number sup{|f(x)|:|x|=r}, where |⋅|(r) is a multiplicative norm on A(K). For another p-adic entire functions g∈A(K), |g|(r) is defined and the ratio |f|(r)|g|(r) as r→∞ is called the comparative growth of f with respect to g in terms of their multiplicative norm. Likewise to complex analysis, in this paper we define the concept of (p,q)th order (respectively (p,q)th lower order) of growth as ρ(p,q)(f)=limsupr→+∞log[p]|f|(r)log[q]r (respectively λ(p,q)(f)=liminfr→+∞log[p]|f|(r)log[q]r), where p and q are any two positive integers. We study then some growth properties of composite p-adic entire functions on the basis of their (p,q)th order and (p,q)th lower order where p and q are any two positive integers.
Authors and Affiliations
T. Biswas
Keywords
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- EP ID EP533003
- DOI 10.15330/cmp.10.2.248-272
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