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
Derivatives of meromorphic functions and exponential functions
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DOI: 10.1007/s11464-018-0691-2
Abstract: We take up a new method to prove a Picard type theorem. Let f be a meromorphic function in the complex plane, whose zeros are multiple, and let R be a Möbius transformation. If $${\overline… read more here.
Keywords: functions exponential; meromorphic functions; derivatives meromorphic; exponential functions ... See more keywords
On the approximation by entire functions of exponential type in $$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