Abstract
AbstractWe review and elaborate on recent work of Chang and Rabinowitz on scaling asymptotics of Poisson and Szegö kernels on Grauert tubes, providing additional results that may be useful in applications. In particular, focusing on the near-diagonal case, we give an explicit description of the leading order coefficients, and an estimate on the growth of the degree of certain polynomials describing the rescaled asymptotics. Furthermore, we allow rescaled asymptotics in a range $$O\left( \lambda ^{\delta -1/2}\right) $$
O
λ
δ
-
1
/
2
in all the variables involved, where $$\lambda \rightarrow +\infty $$
λ
→
+
∞
is the asymptotic parameter, rather than rescale according to Heisenberg type.
Funder
Università di Milano-Bicocca
Università degli Studi di Milano - Bicocca
Publisher
Springer Science and Business Media LLC
Reference51 articles.
1. Bleher, P., Shiffman, B., Zelditch, S.: Universality and scaling of correlations between zeros on complex manifolds. Invent. Math. 142, 351–395 (2000)
2. Boutet de Monvel, L.: Convergence dans le domaine complexe des séries de fonctions propres. (French) C. R. Acad. Sci. Paris Sér. A-B 287(13), A855–A856 (1978)
3. Boutet de Monvel, L.: Convergence dans le domaine complexe des séries de fonctions propres. (French) Journées: Équations aux Dérivées Partielles (Saint-Cast, 1979), Exp. No. 3, 2 pp. École Polytech., Palaiseau (1979)
4. Boutet de Monvel, L., Guillemin, V.: The spectral theory of Toeplitz operators. Annals of Mathematics Studies, vol. 99. Princeton University Press, Princeton; University of Tokyo Press, Tokyo (1981)
5. Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Astérisque, No. 34–35, Société Mathématique de France, Paris, pp. 123–164 (1976)