Boas-Type Formulas and Sampling in Banach Spaces with Applications to Analysis on Manifolds

DOI10.1007/978-3-319-08801-3_3zbMath1408.94910arXiv1311.5995OpenAlexW2525133486MaRDI QIDQ5249763

Isaac Z. Pesenson

Publication date: 12 May 2015

Published in: New Perspectives on Approximation and Sampling Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.5995

zbMATH Keywords

samplingHeisenberg groupSchrödinger representationcompact homogeneous manifoldsexponential and Bernstein vectorsBoas interpolation formula

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Groups and semigroups of linear operators (47D03) Sampling theory in information and communication theory (94A20)

Related Items

Sampling and interpolation for the discrete Hilbert and Kak–Hilbert transforms ⋮ To multidimensional Mellin analysis: Besov spaces, \(K\)-functor, approximations, frames ⋮ Integration of polar-analytic functions and applications to Boas' differentiation formula and Bernstein's inequality in Mellin setting ⋮ Valiron's interpolation formula and a derivative sampling formula in the Mellin setting acquired via polar-analytic functions ⋮ Geometric space-frequency analysis on manifolds ⋮ Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces

Cites Work

• Shannon's sampling theorem for bandlimited signals and their Hilbert transform, Boas-type formulae for higher order derivatives -- the aliasing error involved by their extensions from bandlimited to non-bandlimited signals
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• Analytic vectors
• Paley-Wiener approximations and multiscale approximations in Sobolev and Besov spaces on manifolds
• Paley-Wiener subspace of vectors in a Hilbert space with applications to integral transforms
• Numerical differentiation inspired by a formula of R.P. Boas
• The sampling theorem and linear prediction in signal analysis
• Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds
• Jackson and Bernstein-type inequalities for families of commutative operators in Banach spaces
• Approximation of Besov Vectors by Paley–Wiener Vectors in Hilbert Spaces
• Bernstein-Nikolskii and Plancherel-Polya inequalities in L_p-norms on non-compact symmetric spaces
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• SCALES OF BANACH SPACES
• Limitierungsverfahren von Reihen mehrdimensionaler Kugelfunktionen und deren Saturationsverhalten
• Sampling of band-limited vectors
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