Bernstein spaces, sampling, and Riesz-Boas interpolation formulas in Mellin analysis

DOI10.1007/978-3-031-41130-4_4MaRDI QIDQ6608646

Isaac Z. Pesenson

Publication date: 20 September 2024

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30)

Cites Work

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• On the Paley-Wiener theorem in the Mellin transform setting
• 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
• Mellin analysis and its basic associated metric -- applications to sampling theory
• Numerical differentiation inspired by a formula of R.P. Boas
• The sampling theorem and linear prediction in signal analysis
• A direct approach to the Mellin transform
• Les fonctions conjuguées et les series de Fourier.
• Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome.
• A generalization of the Paley-Wiener theorem for Mellin transforms and metric characterization of function spaces
• 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
• Exponential sampling series: convergence in Mellin-Lebesgue spaces
• Polar-analytic functions: old and new results, applications
• The Mellin–Parseval formula and its interconnections with the exponential sampling theorem of optical physics
• Sampling formulas for one-parameter groups of operators in Banach spaces
• The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley–Wiener theorem for bandlimited signals – their interconnections
• An Irregular Sampling Theorem for Functions Bandlimited in a Generalized Sense
• A sampling theorem for irregularly spaced sample points (Corresp.)
• A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces
• Development of a new concept of polar analytic functions useful in Mellin analysis
• Boas-Type Formulas and Sampling in Banach Spaces with Applications to Analysis on Manifolds
• The Derivative of a Trigonometric Integral

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