Sharp Error Bound on Norm Convergence of Exponential Product Formula and Approximation to Kernels of Schrödinger Semigroups

DOI10.1081/PDE-200040207zbMath1085.47053MaRDI QIDQ4678910

Takashi Ichinose, Hideo Tamura

Publication date: 23 May 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

pseudodifferential operatorsTrotter-Kato formulaSchrödinger semigroupsintegral kernelsoperator norm convergence

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Perturbation theories for operators and differential equations in quantum theory (81Q15) Remainders in approximation formulas (41A80) Schrödinger and Feynman-Kac semigroups (47D08) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (3)

On three magnetic relativistic Schrödinger operators and imaginary-time path integrals ⋮ Note on the norm convergence of the unitary Trotter product formula ⋮ Exponential product approximation to the integral kernel of the Schrödinger semigroup and to the heat kernel of the Dirichlet Laplacian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On error estimates for the Trotter-Kato product formula
• Error bounds on exponential product formulas for Schrödinger operators
• A general calculus of pseudodifferential operators
• Error bounds for Trotter-type formulas for self-adjoint operators
• An estimate of the Kac transfer operator
• Estimate of the difference between the Kac operator and the Schrödinger semigroup
• Error estimate in operator norm for Trotter-Kato product formula
• On the error estimate of the integral kernel for the Trotter product formula for Schrödinger operators
• Trotter--Kato product formula and fractional powers of self-adjoint generators.
• A remark on operator-norm convergence of Trotter-Kato product formula
• Trotter-Kato product formula and operator-norm convergence
• Some remarks on operator-norm convergence of the Trotter product formula on Banach spaces.
• Proprietes spectrales d'operators pseduo-differentiels
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• The norm convergence of the Trotter-Kato product formula with error bound
• Note on the paper: ``The norm convergence of the Trotter--Kato product formula with error bound by T. Ichinose and H. Tamura.

This page was built for publication: Sharp Error Bound on Norm Convergence of Exponential Product Formula and Approximation to Kernels of Schrödinger Semigroups