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

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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.

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Authors and Affiliations

  1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    L. P. Castro & S. Saitoh

  2. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Y. Sawano

  3. Department of Mathematics, University of Beira Interior, 6201l-001, Covilhã, Portugal

    A. M. Simões

Authors
  1. L. P. Castro
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  2. S. Saitoh
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  3. Y. Sawano
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  4. A. M. Simões
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Corresponding author

Correspondence to L. P. Castro.

Additional information

Communicated by Saburou Saitoh.

This work was supported in part by Center for Research and Development in Mathematics and Applications, University of Aveiro, Portugal, through FCT—Portuguese Foundation for Science and Technology.

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Castro, L.P., Saitoh, S., Sawano, Y. et al. General Inhomogeneous Discrete Linear Partial Differential Equations with Constant Coefficients on the Whole Spaces. Complex Anal. Oper. Theory 6, 307–324 (2012). https://doi.org/10.1007/s11785-010-0083-4

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  • DOI: https://doi.org/10.1007/s11785-010-0083-4

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