Discrete orthogonality of the Malmquist Takenaka system of the upper half plane and rational interpolation

DOI10.1007/S00041-013-9285-2zbMath1304.42064OpenAlexW2077244187MaRDI QIDQ485210

Margit Pap, Tímea Eisner

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-013-9285-2

zbMATH Keywords

samplingrational interpolationHardy spacesapproximation by rational functionsdiscrete orthogonalityMalmquist-Takenaka systems

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Approximation by rational functions (41A20) (H^p)-spaces (42B30) Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable (33C50) Numerical methods in Fourier analysis (65T99) Hardy spaces (30H10)

Related Items (11)

Positive-instantaneous frequency and approximation ⋮ Implementation of fractional-order difference via Takenaka-Malmquist functions ⋮ Nonlinear phase unwinding of functions ⋮ Hyperbolic Wavelets ⋮ Phase unwinding, or invariant subspace decompositions of Hardy spaces ⋮ Construction of rational interpolations using Mamquist-Takenaka systems ⋮ Equilibrium conditions for the Malmquist-Takenaka systems ⋮ A Theory on Non-Constant Frequency Decompositions and Applications ⋮ Iterative variable-Blaschke factorization ⋮ A family of orthogonal rational functions and other orthogonal systems with a skew-Hermitian differentiation matrix ⋮ Discrete orthogonality of the analytic wavelets in the Hardy space of the upper half plane

Cites Work

• General sampling theorems for functions in reproducing kernel Hilbert spaces
• \(L^\infty\) system approximation algorithms generated by \(\varphi\) summations
• Intrinsic mono-component decomposition of functions: An advance of Fourier theory
• Reconstruction Algorithms in Irregular Sampling
• BIORTHOGONAL SYSTEMS OF RATIONAL FUNCTIONS AND BEST APPROXIMATION OF THE CAUCHY KERNEL ON THE REAL AXIS
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