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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A partial integration formula for product integrals of unbounded operator-valued functions
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by Rhonda J. Hughes PDF
Proc. Amer. Math. Soc. 96 (1986), 455-461 Request permission

Abstract:

The partial integration formula for product integrals \[ \prod \limits _y^x {{e^{(A(s) + B(s))ds}} = } \prod \limits _y^x {{e^{A(s)ds}}} \prod \limits _y^x {\exp } \left ( {\left ( {\prod \limits _s^y {{e^{A(u)du}}} B(s)\prod \limits _y^s {{e^{A(u)du}}} } \right )ds} \right ),\] of which the Trotter product formula is a consequence, is established for a wide class of unbounded operator-valued functions $A(s),B(s)$.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 455-461
  • MSC: Primary 47D05; Secondary 34G10
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822439-5
  • MathSciNet review: 822439