| Título: | The Norm Estimate of the Difference Between the Kac Operator and Schrödinger Semigroup II: The General Case Including the Relativistic Case |
| Autores: |
Ichinose, Takashi; Kanazawa University Takanobu, Satoshi; Kanazawa University |
| Fecha: | 2000-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Schrödinger operator, Schrödinger semigroup, relativistic Schrödinger operator, Trotter product formula, Lie-Trotter-Kato product formula, Feynman-Kac formula, subordinationof Brownian motion, Kato's inequality 47D07, 35J10, 47F05, 60J65, 60J35 |
| Descripción: | More thorough results than in our previous paper in Nagoya Math. J. are given on the $L_p$-operator norm estimates for the Kac operator $e^{-tV/2} e^{-tH_0} e^{-tV/2}$ compared with the Schrödinger semigroup $e^{-t(H_0+V)}$. The Schrödinger operators $H_0+V$ to be treated in this paper are more general ones associated with the Lévy process, including the relativistic Schrödinger operator. The method of proof is probabilistic based on the Feynman-Kac formula. It differs from our previous work in the point of using the Feynman-Kac formula not directly for these operators, but instead through subordination from the Brownian motion, which enables us to deal with all these operators in a unified way. As an application of such estimates the Trotter product formula in the $L_p$-operator norm, with error bounds, for these Schrödinger semigroups is also derived. |
| Idioma: | No aplica |
1 Lévy Classes and Self-Normalization por Khoshnevisan, Davar; University of Utah | 6 Time-Space Analysis of the Cluster-Formation in Interacting Diffusions por Fleischmann, Klaus; Weierstrass Institute for Applied Analysis and Stochastics,Greven, Andreas; Universitat Erlangen-Nurnberg |
2 Hausdorff Dimension of Cut Points for Brownian Motion por Lawler, Gregory F.; Duke University and Cornell University | 7 Conditional Moment Representations for Dependent Random Variables por Bryc, Wlodzimierz; University of Cincinnati |
3 Eigenvalue Expansions for Brownian Motion with an Application to Occupation Times por Bass, Richard F.; University of Washington,Burdzy, Krzysztof; University of Washington | 8 Almost Sure Exponential Stability of Neutral Differential Difference Equations with Damped Stochastic Perturbations por Liao, Xiao Xin; University of Strathclyde,Mao, Xuerong; University of Strathclyde |
4 Random Discrete Distributions Derived from Self-Similar Random Sets por Pitman, Jim; University of California, Berkeley,Yor, Marc; Université Pierre et Marie Curie | 9 Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes por Roberts, Gareth O.; University of Cambridge,Rosenthal, Jeffrey S.; University of Toronto |
5 A Microscopic Model for the Burgers Equation and Longest Increasing Subsequences por Seppäläinen, Timo; Iowa State University | 10 Metastability of the Three Dimensional Ising Model on a Torus at Very Low Temperatures por Ben Arous, Gérard; Ecole Normale Supérieure,Cerf, Raphaël; Université Paris Sud |