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Title: A fundamental theorem on initial value problems by using the theory of reproducing kernels
Author: Castro, L. P.
Rodrigues, M. M.
Saitoh, S.
Keywords: Initial value problem
Integral transform
Integral equation
Aveiro discretization method
Reproducing kernel
Inverse problem
Issue Date: 2015
Publisher: Springer
Abstract: We introduce a new method for solving general initial value problems by using the theory of reproducing kernels. The results are depending on the specific structure of each problem. Here, we give the general principle of the method and illustrate it with simple prototype examples. On the basis of the process, we have certain integral transforms, which are generated by each specific initial value problem, and need to be analysed. In view of this, we shall establish the basic relations among initial value problems for linear operator equations, eigenvalues and eigenfunctions in the related operator equations, integral transforms and associated reproducing kernels. Within this process, we will realize a general theory for operator equations and incorporate a time dependence in view to consider an associated regularization method.
Peer review: yes
DOI: 10.1007/s11785-014-0375-1
ISSN: 1661-8254
Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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