We study the complexification of Laplace Eigenfunctions on the Grauert tube of a compact real analytic manifold. Our main results concern scaling asymptotics of Fourier coefficients of the Szego kernel on the Grauert tube boundary in a Heisenberg frequency scaled neighborhood of the geodesic flow. We show that in the high frequency limit the Fourier Coefficients are to first order the kernel associated to the quantization of the derivative of the geodesic flow. As an application we provide sharp Lp to Lq mapping estimates for partial Szego kernels on the Grauert Tube boundary and describe their relationship to Husimi distributions of Laplace eigenfunctions.

Creator

• Rabinowitz, Abraham

DOI

• https://doi.org/10.21985/n2-zqer-8j87

Subject

• Mathematics
• Theoretical mathematics

Language

• en

Alternate Identifier

• etdadmin_upload_903279
• http://dissertations.umi.com/northwestern:16093

Date created

• 2022-01-01

Resource type

• Dissertation

Rights statement

• In Copyright