Zeta function regularization: Difference between revisions

Revision as of 00:39, 15 March 2008

Revision as of 05:29, 7 June 2008

Line 49:

:<math>f(s)=\sum_n a_n e^{-s|\omega_n|}</math>

is sometimes called a '''heat kernel''' or a '''heat-kernel regularized sum'''; this name stems from the idea that the <math>\omega_n</math> can sometimes be understood as eigenvalues of the [[heat kernel]]. In mathematics, such a sum is known as a [[generalized Dirichlet series]]; its use for averaging is known as an [[Abelian mean]]. It is closely related to the [[Laplace-Stieltjes transform]], in that

:<math>f(s)=\int_0^\infty e^{-st} d\alpha(t)</math>