Initial Value Problems in Linear Integral Operator Equations

DOI10.1007/978-3-319-06554-0_7zbMath1325.45016OpenAlexW149626537MaRDI QIDQ2945425

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Publication date: 11 September 2015

Published in: Topics in Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10773/16621

zbMATH Keywords

eigenvalueinverse problemintegral transforminversion formulainitial value problemreproducing kerneleigenfunctionFourier integral transformTricomi equationisometric mappingDixon equationLalesco-Picard equationlinear integral operator equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Integral operators (45P05) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Volterra integral equations (45D05) Eigenvalue problems for integral equations (45C05) Integral equations with kernels of Cauchy type (45E05) Linear integral equations (45A05)

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Cites Work

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