Asymptotics of the D ' Alembertian
نویسنده
چکیده
Let be the Laplace-d'Alembert operator on a pseudo-Riemannian manifold (M; g). We derive a series expansion for the fundamental solution G(x; y) of + H , H 2 C 1 (M), which behaves well under various symmetric space dualities. The qualitative properties of this expansion were used in our paper in Invent. Math. 129 (1997) 63{74, to show that the property of vanishing logarithmic term for G(x; y) is preserved under these dualities.
منابع مشابه
Asymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
This paper mainly considers a nonstandard risk model with a constant interest rate, where both the claim sizes and the inter-arrival times follow some certain dependence structures. When the claim sizes are dominatedly varying-tailed, asymptotics for the infinite time ruin probability of the above dependent risk model have been given.
متن کاملAsymptotic Cost of Cutting Down Random Free Trees
In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...
متن کاملInstanton-anti-instanton pair-induced asymptotics of perturbation theory in QCD.
The instanton–antiinstanton pair induced asymptotics of perturbation theory expansion for QCD correlators is considered. It is argued that though the true asymptotics is dominated by renormalon, the instanton-induced contribution may dominate in the intermediate asymptotics n = 5÷ 15. Obtained asymptotic formulae are valid for Nf ≤ Nc. For Nf = Nc the finite nonperturbative expression for insta...
متن کاملAsymptotics of the heat equation with ‘exotic’ boundary conditions or with time dependent coefficients
The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and Dirichlet or Robin boundary conditions.
متن کاملAsymptotics of derivatives of orthogonal polynomials on the unit circle
We show that ratio asymptotics of orthogonal polynomials on the circle imply ratio asymptotics for all their derivatives. Moreover, by reworking ideas of P. Nevai, we show that uniform asymptotics for orthogonal polynomials on an arc of the unit circle imply asymptotics for all their derivatives. Let be a nite positive Borel measure on the unit circle (or [0; 2 ]). Let f'ng denote the orthonor...
متن کامل