The analytic perturbation theory for eigenvalues of Dirac operators on odd dimensional manifolds with boundary is described in terms of [italic]extended L² eigenvectors [end italics] on manifolds with cylindrical ends. These are generalizations of the Atiyah-Patodi-Singer extend…
This memoir is a study of Ray-Singer analytic torsion for hermitian vector bundles on a compact Riemann surface [italic]C. The torsion is expressed through the trace of a modified resolvent. Thus, one can develop perturbation-curvature formulae for the Green-Szegö kernel and al…
The authors show how to interpret recent results of Moser and Veselov on discrete versions of a class of classical integrable systems, in terms of a loop group framework. In this framework the discrete systems appear as time-one maps of integrable Hamiltonian flows. Earlier resu…
The purpose of this article is to fill some part of the gap existing between the mathematical theory of the Navier-Stokes equations and the conventional theory of turbulence and to provide a rigorous connection between these theories.
This paper gives a qualitative analysis of the flow of the anisotropic Kepler problem described by a Hamiltonian system as introduced by Gutzwiller and later studied by Devaney.
This memoir presents a simple sequential definition of the Feynman integral which is applicable to a rather large class of functionals.
This book is based on the notes from lectures given by the second author at Princeton University in the year 1970-71, which were subsequently expanded and revised by the first author.