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Complex Analysis and Operator Theory

, Volume 6, Issue 1, pp 307–324 | Cite as

General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces

  • L. P. CastroEmail author
  • S. Saitoh
  • Y. Sawano
  • A. M. Simões
Article

Abstract

In this paper we shall introduce new constructions of approximate solutions of general linear partial differential equations with constant coefficients on the whole spaces, and establish fundamental estimates of the solutions depending on the inhomogeneous terms. This will be done by combining general ideas of the Tikhonov regularization and discretization of bounded linear operator equations on reproducing kernel Hilbert spaces. Furthermore, we will provide approximate solutions for the related inverse source problems.

Keywords

Linear partial differential equation with constant coefficients Discrete differential equation Approximation of functions Inverse source problem Reproducing kernel Tikhonov regularization Sobolev space Generalized inverse Approximate inverse Error estimate Noise 

Mathematics Subject Classification (2000)

Primary 35A35 Secondary 30C40 35A22 35C15 35E99 46E22 47A52 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • L. P. Castro
    • 1
    Email author
  • S. Saitoh
    • 1
  • Y. Sawano
    • 2
  • A. M. Simões
    • 3
  1. 1.Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal
  2. 2.Department of MathematicsKyoto UniversityKyotoJapan
  3. 3.Department of MathematicsUniversity of Beira InteriorCovilhãPortugal

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