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- W4380886935 abstract "Let f be an entire function, f(0) = 1, F(z) = zf′ (z)/f(z), and Γm = $$bigcup_{j=1}^{m}left{z:mathrm{arg}z={psi }_{j}right},$$ 0 ≤ ψ1 < ψ2 < ...< ψm < 2π. An entire function f is called a function of improved regular growth if for some ρ ∈ (0;+∞) and ρ2 ∈ (0; ρ), and a 2π-periodic ρ-trigonometrically convex function h(φ) ≢ −∞, there exists a set U ⊂ $${mathbb{C}}$$ contained in the union of disks with finite sum of radii such that $$begin{array}{cc}mathrm{log}left|fleft(zright)right|={left|zright|}^{rho }hleft(varphi right)+oleft({left|zright|}^{rho 2}right),& Unotni z={re}^{ivarphi }to infty .end{array}$$ In this paper, we prove that an entire function f of order ρ ∈ (0;+∞) with zeros on a finite system of rays Γm is a function of improved regular growth if and only if for some ρ2 ∈ (0; ρ) and every q ∈ [1;+∞), one has $$begin{array}{cc}{left{frac{1}{2pi }{int }_{0}^{2pi }{left|frac{Fleft({re}^{ivarphi }right)}{{r}^{rho }}|-rho widetilde{h}left(varphi right)right|}^{q}dvarphi right}}^{1/q}=oleft({r}^{rho 2-rho }right),& rto +infty ,end{array}$$ where $$widetilde{h}$$ (φ) = h(φ) − ih′ (φ)/ρ and h(φ) is the indicator of the function f." @default.
- W4380886935 created "2023-06-17" @default.
- W4380886935 creator A5046822603 @default.
- W4380886935 date "2023-06-16" @default.
- W4380886935 modified "2023-09-24" @default.
- W4380886935 title "A criterion for the improved regular growth of an entire function in terms of the asymptotic behavior of its logarithmic derivative in the metric of Lq[0; 2π]" @default.
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- W4380886935 doi "https://doi.org/10.1007/s10958-023-06504-z" @default.
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