We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Scaling Asymptotics for Szegő Kernels on Grauert Tubes.
- Authors
Chang, Robert; Rabinowitz, Abraham
- Abstract
Let M τ be the Grauert tube of radius τ of a closed, real analytic Riemannian manifold M. Associated to the Grauert tube boundary is the orthogonal projection Π τ : L 2 (∂ M τ) → H 2 (∂ M τ) , called the Szegő projector. Let D ρ denote the Hamilton vector field of the Grauert tube function ρ acting as a differential operator. We prove scaling asymptotics for the spectral localization kernel of the Toeplitz operator Π τ D ρ Π τ . We also prove scaling asymptotics for the smoothed spectral projection kernel P χ , λ (z , w) = ∑ λ j ≤ λ χ (λ - λ j) e - 2 τ λ j φ λ j C (z) φ λ j C (w) ¯ , where φ λ j C are CR holomorphic functions on the Grauert tube boundary ∂ M τ , which are obtained by analytically continuing Laplace eigenfunctions on M.
- Subjects
BERGMAN kernel functions; HOLOMORPHIC functions; MATHEMATICS; EIGENFUNCTIONS; NUMERICAL solutions to boundary value problems
- Publication
Journal of Geometric Analysis, 2023, Vol 33, Issue 2, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-022-01116-6