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Real Inversion Formulas of the Laplace Transform

  • Saburou Saitoh
  • Yoshihiro Sawano
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 44)

Abstract

As stated in the preface, one of our strong motivations for writing this book is given by the historical success of the numerical and real inversion formulas of the Laplace transform which is a famous typical ill-posed and very difficult problem. In this chapter, we will see their mathematical theory and formulas, as a clear evidence of the definite power of the theory of reproducing kernels when combined with the Tikhonov regularization.

Keywords

Laplace Transform Tikhonov Regularization Reproduce Kernel Hilbert Space Weighted Sobolev Space Complete Orthonormal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  • Saburou Saitoh
    • 1
  • Yoshihiro Sawano
    • 2
  1. 1.Gunma UniversityKiryuJapan
  2. 2.Department of Mathematics and Information ScienceTokyo Metropolitan UniversityHachiojiJapan

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