Parametrix, kernel asymptotics, and regularized trace for the diffusion semigroup

2008 ◽  
Vol 77 (3) ◽  
pp. 424-427 ◽  
Author(s):  
S. A. Stepin
Keyword(s):  
Regularized Trace ◽  
Diffusion Semigroup

A regularized trace formula for a well-perturbed Laplace operator

2015 ◽  
Vol 91 (1) ◽  
pp. 1-4 ◽  
Author(s):  
B. E. Kanguzhin ◽  
N. E. Tokmagambetov
Keyword(s):  
Laplace Operator ◽  
Trace Formula ◽  
Regularized Trace

scholarly journals Adiabatic limit of the eta invariant over cofinite quotients of PSL(2, ℝ)

2008 ◽  
Vol 144 (6) ◽  
pp. 1593-1616 ◽  
Author(s):  
Paul Loya ◽  
Sergiu Moroianu ◽  
Jinsung Park
Keyword(s):  
Riemann Surface ◽  
Dirac Operator ◽  
Continuous Spectrum ◽  
Spin Structure ◽  
Adiabatic Limit ◽  
Regularized Trace ◽  
Standard Definition ◽  
Eta Invariant ◽  
Hyperbolic Riemann Surface

AbstractThe eta invariant of the Dirac operator over a non-compact cofinite quotient of PSL(2,ℝ) is defined through a regularized trace following Melrose. It reduces to the standard definition in terms of eigenvalues in the case of a totally non-trivial spin structure. When the S1-fibers are rescaled, the metric becomes of non-exact fibered-cusp type near the ends. We completely describe the continuous spectrum of the Dirac operator with respect to the rescaled metric and its dependence on the spin structure, and show that the adiabatic limit of the eta invariant is essentially the volume of the base hyperbolic Riemann surface with cusps, extending some of the results of Seade and Steer.

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