2014/04/08 by James Oldfield, Oldfield, J. P.
Mathematics · #Spectral Theory in Mathematical Physics #Mathematical Analysis and Transform Methods #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1404.2256
This article concerns the asymptotics of pseudodifferential operators whose Weyl symbol is the convolution of a discontinuous function dilated by a large scaling parameter with a smooth function of constant scale. These operators include as a special case generalised anti-Wick operators, also known as Gabor-Toeplitz operators, with smooth windows and dilated discontinuous symbol. The main result is a two-term Szegő theorem, that is, the asymptotics of the trace of a function of the operator. A special case of this is the asymptotic terms of the eigenvalue counting function. In both cases, previously only the first term in the asymptotic expansion was known explicitly.