Roots of complex polynomials and Weyl-Heisenberg frame sets

DOI10.1090/S0002-9939-02-06352-9zbMath0991.42023WikidataQ101069242 ScholiaQ101069242MaRDI QIDQ4529679

Peter G. Casazza, Nigel J. Kalton

Publication date: 6 May 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hilbert spaceZak transformWeyl-Heisenberg frameoptimal frame bounds

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Polynomials in number theory (11C08) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

Related Items (12)

Obituary: Nigel John Kalton, 1946-2010 ⋮ On the abc-problem in Weyl-Heisenberg frames ⋮ The abc-Problem for Gabor Systems and Uniform Sampling in Shift-Invariant Spaces ⋮ Pseudo-Boolean functions and the multiplicity of the zeros of polynomials ⋮ Dilation‐and‐modulation frame sets on the half real line ⋮ When a characteristic function generates a Gabor frame ⋮ On the Multiplicity of the Zeros of Polynomials with Constrained Coefficients ⋮ Weyl-Heisenberg Riesz bases generated by two intervals ⋮ Gabor frame sets for subspaces ⋮ On the Weyl-Heisenberg frames generated by simple functions ⋮ Constructions of Frames by Disjoint Frames ⋮ Characterizations of Wilson systems using roots of polynomials

Cites Work

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• Zeros of polynomials with \(0, 1\) coefficients
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• On the zeros of polynomials with restricted coefficients
• Bargmann transform, Zak transform, and coherent states
• Littlewood-Type Problems on [0,1]
• Frames, bases and group representations
• Continuous and Discrete Wavelet Transforms
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)

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