It is proven that the Trotter product formula converges in the norm of a symmetrically normed ideal of compact operators away from t 0 >0 if the Kac operator (the transfer matrix) F(t)=e &tBΓ2 e &tA e &tBΓ2 belongs to this ideal for t=t 0 . The result is generalized to the Trotter Kato product formu
Multiplicative partial integration and the Trotter Product Formula
β Scribed by P Masani
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 382 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0001-8708
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π SIMILAR VOLUMES
We extend the Trotter-Kato-Chernoff theory of strong approximation of C 0 semigroups on Banach spaces to operator-norm approximation of analytic semigroups with error estimate. As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with
Recently P. Lax has produced a novel approach to the proof of the change of variable formula for multiple integrals. In Section 1 we give a variant of Lax's proof, using the language of differential forms. In Sections 2 and 3 we discuss extensions involving more singular maps and integrands.  2002