On Zeros of Some Entire Functions
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DOI: 10.1007/s00025-019-0978-y
Abstract: Let $$\begin{aligned} A_{q}^{(\alpha )}(a;z)=\sum _{k=0}^{\infty }\frac{(a;q)_{k}q^{\alpha k^2} z^k}{(q;q)_{k}}, \end{aligned}$$Aq(α)(a;z)=∑k=0∞(a;q)kqαk2zk(q;q)k,where $$\alpha >0,~0 read more here.
Keywords: entire functions; zeros entire;
Plancherel–Pólya Inequality for Entire Functions of Exponential Type in L2(ℝ)
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DOI: 10.1007/s10476-018-0104-5
Abstract: We investigate the Plancherel–Pólya inequality $$\sum {_{k \in \mathbb{Z}}} |f(k){|^2} \leqslant {c_2}\left( \sigma \right)||f||_{{L^2}\left( \mathbb{R} \right)}^2$$∑k∈ℤ|f(k)|2⩽c2(σ)||f||L2(ℝ)2 on the set of entire functions f of exponential type at most σ whose restrictions to the real line… read more here.
Keywords: plancherel lya; functions exponential; lya inequality; entire functions ... See more keywords
On Invariant Subspaces of the Pommiez Operator in the Spaces of Entire Functions of Exponential Type
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DOI: 10.1007/s10958-019-04461-0
Abstract: We describe closed invariant eigenspaces of the Pommmiez operator in the (LF)-space of entire functions of exponential type. This space is topologically equivalent (by means of the Laplace transform) to the strong dual space of… read more here.
Keywords: functions exponential; exponential type; operator; entire functions ... See more keywords
Entire functions arising from trees
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DOI: 10.1007/s11425-019-1644-0
Abstract: Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function $f$ with only two critical values $\pm 1$ and no asymptotic values such that $f^{-1}([-1,1])$ is ambiently homeomorphic to… read more here.
Keywords: functions arising; entire functions; arising trees;
On the Uniqueness of Random Entire Functions
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DOI: 10.1007/s11785-021-01123-5
Abstract: Let $$f_\omega (z)=\sum \nolimits _{j=0}^{\infty }\chi _j(\omega ) a_j z^j$$ be a transcendental random entire function, where $$\chi _j(\omega )$$ are independent and identically distributed random variables defined on a probability space $$(\Omega , \mathcal… read more here.
Keywords: uniqueness random; random entire; entire functions;
On the approximation by entire functions of exponential type in $$L_{p,\alpha }(\mathbb {R})$$Lp,α(R)
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DOI: 10.1007/s11868-016-0160-1
Abstract: In this paper, we obtain the direct theorem of approximation of functions on the real line $$\mathbb {R}$$R in the metric of $$L_{p}$$Lp with some power weight using generalized Dunkl shifts. read more here.
Keywords: type alpha; functions exponential; approximation entire; mathbb ... See more keywords
Paley–Wiener properties for spaces of entire functions
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DOI: 10.1007/s13324-020-00361-8
Abstract: We deduce Paley–Wiener results in the Bargmann setting. At the same time we deduce characterisations of Pilipović spaces of low orders. In particular we improve the characterisation of the Gröchenig test function space $$\mathcal {H}_{\flat… read more here.
Keywords: wiener; paley wiener; properties spaces; wiener properties ... See more keywords
On Entire Functions That Share Two Small Functions with Their Derivative
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DOI: 10.1007/s40306-018-0301-0
Abstract: In this paper, we study the relationship between two entire functions sharing two pairs of small functions IM with their derivatives. For such a function f and a positive integer k, we establish a linear… read more here.
Keywords: functions derivative; functions share; small functions; two small ... See more keywords
The largest gap between zeros of entire L-functions is less than 41.54
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DOI: 10.1016/j.jmaa.2016.12.007
Abstract: Abstract Using suitable feasible pairs and convex combinations of Selberg minorant functions, the upper bound under GRH and the Ramanujan hypothesis on the largest gap between consecutive zeros of an entire L -function in Bober,… read more here.
Keywords: entire functions; zeros entire; largest gap; gap zeros ... See more keywords
On transcendental entire functions mapping Q into itself
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DOI: 10.1016/j.jnt.2019.06.018
Abstract: Abstract In this paper, we study a question proposed by Marques and Moreira about transcendental entire functions mapping Q into itself. In particular, we prove that there is no a transcendental entire function f such… read more here.
Keywords: functions mapping; transcendental entire; entire functions;
Sampling of entire functions of several complex variables on a lattice and multivariate Gabor frames
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DOI: 10.1080/17476933.2019.1681415
Abstract: ABSTRACT We give a general construction of entire functions in d complex variables that vanish on a lattice of the form for an invertible complex-valued matrix. As an application, we exhibit a class of lattices… read more here.
Keywords: sampling entire; several complex; complex variables; functions several ... See more keywords