Bounding partial sums of Fourier series in weighted \(L^{2}\)-norms, with applications to matrix analysis

DOI10.1016/S0377-0427(02)00441-7zbMath1014.42005OpenAlexW2012218352MaRDI QIDQ1860415

Natalia Borovykh, Marc N. Spijker

Publication date: 23 February 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(02)00441-7

zbMATH Keywords

Toeplitz matrixFourier seriespartial sumsresolvent conditionKreiss matrix theoremweighted normHelson-Szegő condition

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

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Cites Work

• On a conjecture by LeVeque and Trefethen related to the Kreiss matrix theorem
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• A problem in prediction theory
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• About the sharpness of the stability estimates in the Kreiss matrix theorem
• On the norm of a finite boolean algebra of projections, and applications to theorems of Kreiss and Morton
• Weighted Norm Inequalities for the Conjugate Function and Hilbert Transform
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