Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/13977
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 Eigenfunction Eigenvalue 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 |
URI: | http://hdl.handle.net/10773/13977 |
DOI: | 10.1007/s11785-014-0375-1 |
ISSN: | 1661-8254 |
Appears in Collections: | CIDMA - Artigos FAAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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PostPrint_IVP.pdf | Article | 149.03 kB | Adobe PDF | View/Open |
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