ABSTRACT

  We study multidimensional generalisations of the classical
Wiener-Hopf operators interpreting them as pseudo-differential operators
with symbols having jump discontinuities on some surfaces in R^d, d\ge 1.
The main objective is to justify a two-term quasi-classical
asymptotic formula for the trace tr(g(T)) where T is the operator at hand,
and g is some function.

  For smooth discontinuity surfaces and smooth functions g the sought 
formula was proved by A. Sobolev in 2009. The aim of this talk is to
extend this result to piece-wise smooth surfaces, and to non-smooth functions g.
These generalizations are of interest in Mathematical Physics and
Quantum Information Theory.

  A part of this work was done in collaboration with H. Leschke and W. Spitzer.