scholarly journals The Generalized heat function

2007 ◽  
Vol 34 (21) ◽  
Author(s):  
Richard J. Greatbatch ◽  
Xiaoming Zhai
Keyword(s):  
Heat Function

scholarly journals On the Inversion of the Specific-Heat Function

1959 ◽  
Vol 22 (4) ◽  
pp. 526-530 ◽  
Author(s):  
George Weiss
Keyword(s):  
Specific Heat ◽  
Heat Function

Asymptotics for the spectral heat function and bounds for integrals of Dirichlet eigenfunctions

1999 ◽  
Vol 129 (4) ◽  
pp. 841-854 ◽  
Author(s):  
M. van den Berg ◽  
S. P. Watson
Keyword(s):  
Riemannian Manifold ◽  
Smooth Boundary ◽  
Beltrami Operator ◽  
Heat Function

We introduce the spectral heat function H associated with the Dirichlet-Laplace–Beltrami operator ΔM on a compact smooth Riemannian manifold M with a non-empty smooth boundary. We obtain two-term asymptotics for H without assuming any billiard conditions on M. As a corollary, we obtain estimates for the integral of the k′th Dirichlet eigenfunction of ΔM over M for k→∞.

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