A family of orthogonal rational functions and other orthogonal systems with a skew-Hermitian differentiation matrix

DOI10.1007/s00041-019-09718-5zbMath1459.42006arXiv1911.08917OpenAlexW2990838456WikidataQ126303540 ScholiaQ126303540MaRDI QIDQ2291572

Marcus Webb, Arieh Iserles

Publication date: 31 January 2020

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

Full work available at URL: https://arxiv.org/abs/1911.08917

zbMATH Keywords

fast Fourier transformorthogonal rational functionsspectral methodsorthogonal systemsMalmquist-Takenaka system

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Related Items (6)

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials ⋮ Approximation of wave packets on the real line ⋮ Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices ⋮ Computing Semigroups with Error Control ⋮ Analytical properties of the generalized heat matrix polynomials associated with fractional calculus ⋮ A differential analogue of Favard's theorem

Uses Software

• DLMF
• OPQ

Cites Work

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• Numerical stability in the presence of variable coefficients
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• The joy and pain of skew symmetry
• Exact errors of best approximation for complex-valued nonperiodic functions
• Spectral methods using rational basis functions on an infinite interval
• Orthogonal systems with a skew-symmetric differentiation matrix
• Local approximations based on orthogonal differential operators
• Equilibrium conditions for the Malmquist-Takenaka systems
• Chromatic expansions of generalized functions
• Chromatic expansions in function spaces
• Algebraic and Spectral Properties of General Toeplitz Matrices
• Generalizations of Chromatic Derivatives and Series Expansions
• Computing the Hilbert Transform on the Real Line
• A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space

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