目次

- Part I Preliminaries.- Semigroups and their generators.- Linear Evolution Equations.- Quasi-sectorial contractions and operator-norm convergence.- Part II: Trotter-Kato product formulæ for self-adjoint semigroups.- Product approximations of self-adjoint semigroups.- Trotter-Kato product formulæ: strong operator topology.- Trotter-Kato product formulæ: operator-norm topology.- Trotter-Kato product formulae: operator-norm topology and error bounds.- Part III: Trotter-Kato product formulæ for non-self-adjoint semigroups.- Operator-norm approximation theory `a la Cherno .- Product formulæ for non-self-adjoint semigroups.- Operator-norm Trotter product formula on Banach spaces.- Part IV: Time-dependent product formulæ. - Time-dependent product formulæ: Banach space.- Time-dependent product formulæ: Hilbert space.- Part V: Unitary and Zeno product formulæ.- Unitary product formulæ. - Zeno product formulæ.