Trotter--Kato product formula for unitary groups
- Exner, Pavel
- Neidhardt, Hagen
2010 Mathematics Subject Classification
- 47A55, 47D03, 81Q30, 32A40 47B25
- Trotter product formula, Trotter-Kato product formula, unitary groups, Feynman path integrals, holomorphic Kato functions
Let $A$ and $B$ be non-negative self-adjoint operators in a separable Hilbert space such that its form sum $C$ is densely defined. It is shown that the Trotter product formula holds for imaginary times in the $L^2$-norm. The result remains true for the Trotter-Kato product formula for so-called holomorphic Kato functions; we also derive a canonical representation for any function of this class.
- Integral Equations Operator Theory, 69 (2011) pp. 451--478.