Generalized types of the growth of Dirichlet series
Journal Title: Карпатські математичні публікації - Year 2015, Vol 7, Issue 2
Abstract
Let A∈(−∞,+∞] and Φ be a continuously on [σ0,A) function such that Φ(σ)→+∞ as σ→A−0. We establish a necessary and sufficient condition on a nonnegative sequence λ=(λn), increasing to +∞, under which the equality ¯¯¯¯¯¯¯¯limσ↑AlnM(σ,F)Φ(σ)=¯¯¯¯¯¯¯¯limσ↑Alnμ(σ,F)Φ(σ), holds for every Dirichlet series of the form F(s)=∑∞n=0anesλn, s=σ+it, absolutely convergent in the half-plane Res<A, where M(σ,F)=sup{|F(s)|:Res=σ} and μ(σ,F)=max{|an|eσλn:n≥0} are the maximum modulus and maximal term of this series respectively.
Authors and Affiliations
T. Ya. Hlova, P. V. Filevych
Keywords
Related Articles
- EP ID EP541766
- DOI 10.15330/cmp.7.2.172-187
- Views 69
- Downloads 0
A realization of the uncertainty principle
We obtain the statement about the imitation behavior of the sum of functions on the real half-line by each of the summands under some conditions for these functions and their Laplace transforms.
Some analytic properties of the Weyl function of a closed linear relation
Let L and L0, where L is an expansion of L0, be closed linear relations (multivalued operators) in a Hilbert space H. In terms of abstract boundary operators (i.e. in the form which in the case of differential operators...
On the similarity of matrices AB and BA over a field
Let A and B be n-by-n matrices over a field. The study of the relationship between the products of matrices AB and BA has a long history. It is well-known that AB and BA have equal characteristic polynomials (and, theref...
Translation, modulation and dilation systems in set-valued signal processing
In this paper, we investigate a very important function space consists of set-valued functions defined on the set of real numbers with values on the space of all compact-convex subsets of complex numbers for which the pt...
On a necessary condition for Lp (0<p<1) -convergence (upper boundedness) of trigonometric series
In this paper we prove that the condition ∑2nk=[n2]λk(p)(|n−k|+1)2−p=o(1)(=O(1)), is a necessary condition for the Lp(0<p<1)-convergence (upper boundedness) of a trigonometric series. Precisely, the results extend some r...