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Integral Equations and Operator Theory

, Volume 27, Issue 2, pp 195–207 | Cite as

Error estimate in operator norm for Trotter-Kato product formula

  • Takashi Ichinose
  • Hideo Tamura
Article

Abstract

In the present paper we study the error estimate in the operator norm for the Trotter-Kato product formula, having an intention to apply the obtained result to Schrödinger semigroups with singular potentials.

AMS Classification Numbers:

Primary 47D03 Secondary 35K22 41A80 

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References

  1. 1.
    P. R. Chernoff, Note on product formulas for operator semigroups,J. Func. Anal., 2: 238–242 (1968).Google Scholar
  2. 2.
    T. Kato, Trotter's product formula for an arbitrary pair of self-adjoint contraction semigroup,Topics in Func. Anal., Adv. Math. Suppl. Studies, 3: 185–195 (1978).Google Scholar
  3. 3.
    D. L. Rogava, Error bounds for Trotter-type formulas for self-adjoint operators,Func. Anal. Appl., 27: 217–219 (1993).Google Scholar
  4. 4.
    H. F. Trotter, On the product of semigroups of operators,Proc. Am. Math. Soc., 10: 545–551 (1959).Google Scholar
  5. 5.
    T. Ichinose and H. Tamura, Error bound in trace norm for Trotter-Kato product formula of Gibbs semigroups, Preprint, Kanazawa and Ibaraki Universities, 1996.Google Scholar

Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Takashi Ichinose
    • 1
  • Hideo Tamura
    • 2
  1. 1.Department of MathematicsKanazawa UniversityKanazawaJapan
  2. 2.Department of MathematicsIbaraki UniversityIbaraki 310Japan

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