APPLICATIONS OF THE REPRODUCING KERNEL THEORY TO INVERSE PROBLEMS

  • Saitoh, Saburou (Department of Mathematics, Faculty of Engineering, Gunma University)
  • Published : 2001.07.01

Abstract

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

Keywords

References

  1. Complex Variables v.15 The Bergman space on a sector and the heat equation H. Aikawa;N. Hayashi;S. Saitoh
  2. J. Math. Soc. Japan v.43 Isometrical identities for the Bergman and the Szego spaces on a sector H. Aikawa;N. Hayashi;S. Saitoh
  3. Zeitschrift fur Analysis und ihre Anwendungen v.18 a real inversion formula for the Laplace transform in a Sovolev space K. Amano;S. Saitoh;A. Syarif
  4. Preprint Series;Graduate School of Math Sci. Error estimates of the real inversion formulas of the Laplace transform K. Amano;S. Saitoh;M. Yamamoto
  5. Zeitschrift fur Analysis und ihre Anwendungen v.12 A real inversiom formula for the Laplace transform D. W. Byun;S. Saitoh
  6. J. Approximation Theory v.78 Approximation by by the solutions of the heat equation D. W. Byun;S. Saitoh
  7. Proc. of the 2th International Colloquium on Numerical Analysis Best approximation in reproducing kernel Hilbert spaces D. W. Byun;S. Saitoh
  8. Complex Variables v.26 Analytic extensions of functions on the real line to entire functions D. W. Byun;S. Saitoh
  9. Ann. Inst. Henri Poincare v.52 Analyticity and global existence of smoothing effect for the Schrodinger equation N. Hayashi;S. Saitoh
  10. Commun. Math. Phys. v.139 Analyticity and global existence of small solutions to some nonlinear Schrodinger equation N. Hayashi;S. Saitoh
  11. Proceedings of the second Korean-Japanese Colloquiumor Finite or Infinite Dimensional Complex Analysis Program for the numerical analysis of inverse formula for the Laplace transform J. Kajiwara;M. Tsuji
  12. Proceedings of the 5th International Colloquium on Differential Equatation Inverse formula for Laplace transform J. Kajiwara;M. Tsuji
  13. Inverse Problems v.15 Representations of initial heat distributions by means of their heat distributions as functions of time G. Nakamura;S. Saitoh;A. Syarif
  14. Proc. Amer. Math Soc. v.89 Hilbert spaces induced by Hilbert space valued functions S. Saitoh
  15. Applicable Analysis v.16 The Weierstrass transform and an isometry in the heat equation S. Saitoh
  16. Applicable Analysis v.17 Some fundamental interpolation problems for analytic and harmonic functions of class L₂ S. Saitoh
  17. Pitman Research Notes in Mathematics Series Theory of Reproducing Kernels and its Aplications S. Saitoh
  18. Pitman Research Notes in Mathematics Series v.212 Interpolation problems of Pick-Nevanlinna type S. Saitoh
  19. Applicable Analysis v.40 Isometrical identities and inverse formulas in the one-dimentional heat equation S. Saitoh
  20. Complex Variables v.19 Representations of the norms in Bergman-Selberg spaces on strips and half planes S. Saitoh
  21. Integral Transforms and Special Functions v.3 One approach to some general integral transforms and its applications S. Saitoh
  22. General Inequalities v.7 Natural norm inequalities in nonlinear transforms S. Saitoh
  23. Proc. Amer. Math. Soc. v.125 Representations of inverse functions S. Saitoh
  24. Pitman Research Notes in Mathematics Series Integral Transforms S. Saitoh
  25. Nonlinear Mathematical Analysis and Applications Nonlinear transforms and analyticity of functions S. Saitoh
  26. International J. of Applied Math. v.1 Various operators in Hilbert space induced by transforms S. Saitoh
  27. J. of Inequa & Appl. v.1 Stability of Lipschitz type in determinational of initial heat distribution S. Saitoh;M. Yamamoto
  28. Integral transforms involving smooth functions v.1 S. Saitoh;M. Yamamoto
  29. Volterra Equations and Applications Linear integro-differential equatations and the theory of reproducing kernels S. Saitoh;C. Corduneanu(ed.);I. W. Sandberg(ed.)
  30. Applicable Analysis v.74 Size of support of initial heat distribution in the ID heat equation V. K. Than;S. Saitoh;M. Saigo