Electronic Journal of Differential Equations,
Conference 04 (2000), pp.  87-101.

Title: Spectral Riesz--Cesaro means: How the square root function helps us 
to see around the world

Authors: S. A. Fulling (Texas A&M Univ., College Station, TX, USA)
  E. V. Gorbar (Instituto di Fisica Teorica, Sao Paulo, Brazil)
  C. T. Romero (Texas A&M Univ., College Station, TX, USA)
 
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.
Math Subject Classifications: 35P20, 40G05, 81Q10.
Key Words: Riesz means; spectral asymptotics; heat kernel; line bundle.