Natural outputs and global inputs of linear systems with a finite number of input data

DOI10.1080/00036811.2010.549484zbMath1237.44004OpenAlexW1980355290MaRDI QIDQ3225838

Luis Filipe Pinheiro de Castro, Saburou Saitoh

Publication date: 22 March 2012

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2010.549484

zbMATH Keywords

Sobolev spacewave equationheat conductionreproducing kernel Hilbert spacesreproducing kernelgeneralized inversesampling theoryTikhonov regularizationdiscrete dataPaley-Wiener spaceapproximate inverseGaussian convolutionapproximation of functionforward problemWeierstrass transformsensibility of system

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Heat equation (35K05) Wave equation (35L05) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22)

Cites Work

• The weierstrass transform and an isometry in the heat equation
• Approximate real inversion formulas of the gaussian convolution
• Numerical real inversion of the Laplace transform by reproducing kernel and multiple-precision arithmetic
• Approximate and analytical inversion formulas in heat conduction on multidimensional spaces
• Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces

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