S. A. Fulling, E. V. Gorbar, & C. T. Romero
Abstract:
The heat-kernel expansion for a nonanalytic function of a
differential operator, and the integrated (Cesàro-smoothed)
spectral densities associated with
the corresponding nonanalytic function of the spectral parameter,
exhibit a certain nonlocal behavior.
Because of this phenomenon, care is needed in applying the
pseudodifferential symbolic calculus to nonanalytic functions.
We demonstrate this effect by both analytical and numerical
calculations for the square root of the Laplace operator
in the model of a "twisted" scalar field
over the circle. This shows that the effect cannot be attributed
solely to boundaries.
Published July 12, 2000.
Mathematics Subject Classifications: 35P20, 40G05, 81Q10.
Key words: Riesz means, spectral asymptotics, heat kernel,
line bundle.
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S. A. Fulling Department of Mathematics Texas A&M University College Station, Texas 77843-3368 e-mail: fulling@math.tamu.edu |
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E. V. Gorbar Instituto di Fisica Teorica Rua Pamplona, 145 0145-900, São Paulo, Brazil e-mail: gorbar@ift.unesp.br |
| C. T. Romero Department of Computer Science Texas A&M University College Station, Texas 77843-3112 e-mail: cromero@tamu.edu |