A partial integration formula for product integrals of unbounded operator-valued functions

Hughes, Rhonda J.

doi:10.1090/S0002-9939-1986-0822439-5

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 $A(s),B(s)$.

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