WIAS Preprint No. 1428, (2009)

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.

Appeared in

  • Integral Equations Operator Theory, 69 (2011) pp. 451--478.

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