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Inversion of Chernoff’s theorem

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Abstract

In this paper, we prove a theorem which is the inversion of Chernoff’s theorem. As a consequence of this result, we obtain conditions for the validity of the Chernoff and Trotter product formulas.

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References

  1. P. R. Chernoff, “Note on product formulas for operator semigroups,” J. Funct. Anal. 2(2), 238–242 (1968).

    Article  MATH  MathSciNet  Google Scholar 

  2. E. B. Davies, One-Parameter Semigroups, in London Math. Soc. Monogr. (Academic Press, London-New York, 1980), Vol. 15.

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  3. O. G. Smolyanov and E. T. Shavgulidze, Path Integrals (Izd. Moskov. Univ., Moscow, 1990) [in Russian].

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  4. O. G. Smolyanov, A. G. Tokarev, and A. Truman, “Hamiltonian Feynman path integral via Chernoff formula,” J. Math. Phys. 43(10), 5161–5171 (2002).

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  5. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, in Grad. Texts in Math. (Springer-Verlag, New York, 2000), Vol. 194.

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Correspondence to A. Yu. Neklyudov.

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Original Russian Text © A. Yu. Neklyudov, 2008, published in Matematicheskie Zametki, 2008, Vol. 83, No. 4, pp. 581–589.

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Neklyudov, A.Y. Inversion of Chernoff’s theorem. Math Notes 83, 530–538 (2008). https://doi.org/10.1134/S0001434608030267

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  • DOI: https://doi.org/10.1134/S0001434608030267

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