Indexing metadata

The Norm Estimate of the Difference Between the Kac Operator and Schrödinger Semigroup II: The General Case Including the Relativistic Case


 
Dublin Core PKP Metadata Items Metadata for this Document
 
1. Title Title of document The Norm Estimate of the Difference Between the Kac Operator and Schrödinger Semigroup II: The General Case Including the Relativistic Case
 
2. Creator Author's name, affiliation, country Takashi Ichinose; Kanazawa University
 
2. Creator Author's name, affiliation, country Satoshi Takanobu; Kanazawa University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Schrödinger operator, Schrödinger semigroup, relativistic Schrödinger operator, Trotter product formula, Lie-Trotter-Kato product formula, Feynman-Kac formula, subordinationof Brownian motion, Kato's inequality
 
3. Subject Subject classification 47D07, 35J10, 47F05, 60J65, 60J35
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2000-01-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/61
 
10. Identifier Digital Object Identifier 10.1214/EJP.v5-61
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 5
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
15. Rights Copyright and permissions The Electronic Journal of Probability applies the Creative Commons Attribution License (CCAL) to all articles we publish in this journal. Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles published in EJP, so long as the original authors and source are credited. This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.

Summary of the Creative Commons Attribution License

You are free
  • to copy, distribute, display, and perform the work
  • to make derivative works
  • to make commercial use of the work
under the following condition of Attribution: others must attribute the work if displayed on the web or stored in any electronic archive by making a link back to the website of EJP via its Digital Object Identifier (DOI), or if published in other media by acknowledging prior publication in this Journal with a precise citation including the DOI. For any further reuse or distribution, the same terms apply. Any of these conditions can be waived by permission of the Corresponding Author.