SINGULAR-VALUES OF COMPACT PSEUDODIFFERENTIAL-OPERATORS

This paper investigates the asymptotic decay of the singular values of compact operators arising from the Weyl correspondence. The motivatin g problem is to find sufficient conditions on a symbol which ensure th at the corresponding operator has singular values with a prescribed ra te of decay. The problem is approached by using a Gabor frame expansio n of the symbol to construct an approximating finite rank operator. Th is establishes a variety of sufficient conditions for the associated o perator to be in a particular Schatten class. In particular, an improv ement of a sufficient condition of Daubechies for an operator to be tr ace-class is obtained. In addition, a new development and improvement of the Calderon-Vaillancourt theorem in the context of the Weyl corres pondence is given. Additional results of this type are then obtained b y interpolation. (C) 1997 Academic Press.