A fundamental theorem on initial value problems by using the theory of reproducing kernels

DOI10.1007/s11785-014-0375-1zbMath1342.47088OpenAlexW2056660368MaRDI QIDQ2514171

Yanyan Li

Publication date: 2 February 2015

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

Full work available at URL: http://hdl.handle.net/10773/13977

zbMATH Keywords

eigenvalueinverse problemintegral equationintegral transforminitial value problemreproducing kerneleigenfunctionAveiro discretization method

Mathematics Subject Classification ID

Applications of operator theory to differential and integral equations (47N20) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Inverse problems for integral equations (45Q05) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (4)

A unified reproducing kernel method and error estimation for solving linear differential equation with functional constraints ⋮ Initial Value Problems in Linear Integral Operator Equations ⋮ A Reproducing Kernel Theory with Some General Applications ⋮ Solutions of Tikhonov functional equations and applications to multiplication operators on Szegő spaces

Cites Work

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• Optimal and approximate solutions of singular integral equations by means of reproducing kernels
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• Hilbert Spaces Induced by Hilbert Space Valued Functions
• How to Catch Smoothing Properties and Analyticity of Functions by Computers?
• Aveiro Discretization Method in Mathematics: A New Discretization Principle
• Theory of Reproducing Kernels

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