English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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 Schrodinger semigroup $e^{-t(H_0+V)}$. The Schrodinger operators $H_0+V$ to be treated in this paper are more general ones associated with the Levy process, including the relativistic Schrodinger 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 Schrodinger semigroups is also derived.

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