Reflection positivity on real intervals
From MaRDI portal
Publication:1639998
DOI10.1007/S00233-017-9847-8zbMATH Open1407.43003arXiv1608.04010OpenAlexW2964082861MaRDI QIDQ1639998
Author name not available (Why is that?)
Publication date: 13 June 2018
Published in: (Search for Journal in Brave)
Abstract: We study functions f : (a,b) ---> R on open intervals in R with respect to various kinds of positive and negative definiteness conditions. We say that f is positive definite if the kernel f((x + y)/2) is positive definite. We call f negative definite if, for every h > 0, the function e^{-hf} is positive definite. Our first main result is a L'evy--Khintchine formula (an integral representation) for negative definite functions on arbitrary intervals. For (a,b) = (0,infty) it generalizes classical results by Bernstein and Horn. On a symmetric interval (-a,a), we call f reflection positive if it is positive definite and, in addition, the kernel f((x - y)/2) is positive definite. We likewise define reflection negative functions and obtain a L'evy--Khintchine formula for reflection negative functions on all of R. Finally, we obtain a characterization of germs of reflection negative functions on 0-neighborhoods in R.
Full work available at URL: https://arxiv.org/abs/1608.04010
No records found.
No records found.
This page was built for publication: Reflection positivity on real intervals
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1639998)
