Mathematical Physics and Quantum Field Theory
Electron. J. Diff. Eqns., Conf. 04, 2000, pp. 87101.
Spectral RieszCesàro means:
How the square root function helps us to see around the world
S. A. Fulling, E. V. Gorbar, & C. T. Romero
Abstract:
The heatkernel expansion for a nonanalytic function of a
differential operator, and the integrated (Cesàrosmoothed)
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 778433368
email: fulling@math.tamu.edu 

E. V. Gorbar
Instituto di Fisica Teorica
Rua Pamplona, 145
0145900, São Paulo, Brazil
email: gorbar@ift.unesp.br 

C. T. Romero
Department of Computer Science
Texas A&M University
College Station, Texas 778433112
email: cromero@tamu.edu 
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Electr. J. Diff. Eqns.