General inhomogeneous discrete linear partial differential equations with constant coefficients on the whole spaces

DOI10.1007/s11785-010-0083-4zbMath1273.35017OpenAlexW1976927997MaRDI QIDQ371650

Yoshihiro Sawano, Saburou Saitoh, Luis Filipe Pinheiro de Castro, Alberto M. Simões

Publication date: 10 October 2013

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-010-0083-4

zbMATH Keywords

noiseSobolev spaceerror estimatereproducing kernelgeneralized inverseTikhonov regularizationinverse source problemapproximate inverseapproximation of functionsdiscrete differential equationlinear partial differential equation with constant coefficients

Mathematics Subject Classification ID

Integral representations of solutions to PDEs (35C15) 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) Linear operators and ill-posed problems, regularization (47A52) Partial differential equations and systems of partial differential equations with constant coefficients (35E99)

Related Items (9)

Fractional functions and their representations ⋮ Extremal functions on Sturm-Liouville hypergroups ⋮ Reproducing kernel theory associated with the generalized Stockwell transform and applications ⋮ Optimal and approximate solutions of singular integral equations by means of reproducing kernels ⋮ Discrete linear differential equations ⋮ Cherednik-Sobolev spaces and applications ⋮ \(k\)-Hankel Gabor transform on \(\mathbb{R}^d\) and its applications to the reproducing kernel theory ⋮ Extremal functions on Sobolev–Dunkl spaces ⋮ Sobolev spaces associated with a Dunkl type differential-difference operator on the real line and applications

Cites Work

• Source inversion of heat conduction from a finite number of observation data
• Hilbert Spaces Induced by Hilbert Space Valued Functions
• Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces
• Dirichlet principle using computers
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