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The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals
Author(s) -
Albeverio Sergio,
De MonvelBerthier Anne Boutet,
Brzeźniak Zdzislaw
Publication year - 1996
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19961820103
Subject(s) - mathematics , bounded function , semigroup , trace (psycholinguistics) , countable set , quadratic equation , constant (computer programming) , nonlinear system , computation , pure mathematics , mathematical analysis , quantum mechanics , physics , geometry , algorithm , computer science , programming language , philosophy , linguistics
Abstract The theory of infinite dimensional oscillatory integrals by finite dimensional approximations is shown to provide new information on the trace formula for Schrödinger operators. In particular, the explicit computation of contributions given by constant and non constant periodic orbits, for potentials which are quadratic plus a bounded nonlinear part, is provided. The heat semigroup as well as the Schrödinger group are discussed and it is shown in particular that their singular supports are contained in an explicit countable set independent of the bounded part of the potential.