Reflection positivity on real intervals

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Jorgensen PE, Neeb KH, Olafsson G
Zeitschrift: Semigroup Forum
Jahr der Veröffentlichung: 2018
Band: 96
Seitenbereich: 31-48
ISSN: 0037-1912


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.


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Neeb, Karl-Hermann Prof. Dr.
Lehrstuhl für Mathematik (Lie-Gruppen und Darstellungstheorie)


Einrichtungen weiterer Autorinnen und Autoren

Louisiana State University
University of Iowa


Zitierweisen

APA:
Jorgensen, P.E., Neeb, K.-H., & Olafsson, G. (2018). Reflection positivity on real intervals. Semigroup Forum, 96, 31-48. https://dx.doi.org/10.1007/s00233-017-9847-8

MLA:
Jorgensen, Palle E.T., Karl-Hermann Neeb, and Gestur Olafsson. "Reflection positivity on real intervals." Semigroup Forum 96 (2018): 31-48.

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Zuletzt aktualisiert 2019-30-01 um 12:08