A note on the Wodzicki residue

✍ Scribed by Thomas Ackermann

• Book ID: 104343374
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 176 KB
• Volume: 20
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(95)00061-5

✦ Synopsis

In this note we explain the relationship of the Wodzicki residue of (certain powers of) an elliptic differential operator P acting on sections of a complex vector bundle E over a closed compact manifold M and the asymptotic expansion of the trace of the corresponding heat operator eTrP. In the special case of a generalized laplacian A and dim h4 > 2, we thereby obtain a simple proof of the fact already shown in [KW], that the Wodzicki residue res(A-"/2+') is the integral of the second coefficient of the heat kernel expansion of A up to a proportional factor.