Singular Values of Compact Pseudodifferential Operators

✍ Scribed by C Heil; J Ramanathan; P Topiwala

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 420 KB
• Volume: 150
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3127

✦ Synopsis

This paper investigates the asymptotic decay of the singular values of compact operators arising from the Weyl correspondence. The motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay. The problem is approached by using a Gabor frame expansion of the symbol to construct an approximating finite rank operator. This establishes a variety of sufficient conditions for the associated operator to be in a particular Schatten class. In particular, an improvement of a sufficient condition of Daubechies for an operator to be trace-class is obtained. In addition, a new development and improvement of the Caldero n Vaillancourt theorem in the context of the Weyl correspondence is given. Additional results of this type are then obtained by interpolation.