Plancherel–Pólya Inequality for Entire Functions of Exponential Type in L2(ℝ)

We investigate the Plancherel–Pólya inequality ∑ k ∈ ℤ | f ( k ) | 2 ⩽ c 2 ( σ ) | | f | | L 2 ( ℝ ) 2 on the set of entire functions f of exponential type at most σ whose restrictions to the real line belong to the space L 2 (ℝ). We prove that c 2 ( σ ) = [ σ / π ] for σ > 0 and describe the ext...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2018-03, Vol.44 (1), p.43-50
Main Author: Berestova, E. V.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:We investigate the Plancherel–Pólya inequality ∑ k ∈ ℤ | f ( k ) | 2 ⩽ c 2 ( σ ) | | f | | L 2 ( ℝ ) 2 on the set of entire functions f of exponential type at most σ whose restrictions to the real line belong to the space L 2 (ℝ). We prove that c 2 ( σ ) = [ σ / π ] for σ > 0 and describe the extremal functions.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-018-0104-5