IJPAM: Volume 15, No. 1 (2004)
SEMICLASSICAL ASYMPTOTICS OF THE TRACE
OF THE HEAT KERNEL FOR THE SCHRÖDINGER
OPERATOR WITH A DEGENERATE POTENTIAL
OF THE HEAT KERNEL FOR THE SCHRÖDINGER
OPERATOR WITH A DEGENERATE POTENTIAL
Junichi Aramaki
Department of Mathematical Sciences
Faculty of Science and Engineering
Tokyo Denki University
Hotoyama-Machi, Hiki-Gun
Saitama-Ken, 350-0394, JAPAN
Department of Mathematical Sciences
Faculty of Science and Engineering
Tokyo Denki University
Hotoyama-Machi, Hiki-Gun
Saitama-Ken, 350-0394, JAPAN
Abstract.We consider the effect of a magnetic field for the semiclassical asymptotics of the trace of the heat kernel for the Schrödinger operator. We discuss the case where the operator has compact resolvents in spite of the fact that the electric potential is degenerate on some submanifold. According to the degree of the degeneracy, we obtain the various semiclassical asymptotics of eigenvalues.
Received: June 10, 2004
AMS Subject Classification: 35J10, 35P20
Key Words and Phrases: magnetic field, Schrödinger operator, semiclassical asymptotics, compact resolvents,
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 15
Issue: 1
