(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
Related Articles
- EP ID EP533003
- DOI 10.15330/cmp.10.2.248-272
- Views 68
- Downloads 0
A Worpitzky boundary theorem for branched continued fractions of the special form
For a branched continued fraction of a special form we propose the limit value set for the Worpitzky-like theorem when the element set of the branched continued fraction is replaced by its boundary.
Some classes of dispersible dcsl-graphs
A distance compatible set labeling dcsl of a connected graph G is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a non empty ground set, such that the corresponding induced function $f^{\oplus} :E(G)...
The structure of solutions of the matrix linear unilateral polynomial equation with two variables
We investigate the structure of solutions of the matrix linear polynomial equation $A(\lambda)X(\lambda)+B(\lambda)Y(\lambda)=C(\lambda),$\ in particular, possible degrees of the solutions. The solving of this equation...
Representation of spectra of algebras of block-symmetric analytic functions of bounded type
The paper contains a description of a symmetric convolution of the algebra of block-symmetric analytic functions of bounded type on $\ell_1$-sum of the space $\mathbb{C}^2$. We show that the specrum of such algebra does...
Geometry of hypersurfaces of a quarter symmetric non metric connection in a quasi-Sasakian manifold
The purpose of the paper is to study the notion of CR-submanifold and the existence of some structures on a hypersurface of a quarter symmetric non metric connection in a quasi-Sasakian manifold. We study the existence o...