6 papers
Spectrum of the d-bar-Neumann Laplacian on polydiscs
Siqi Fu
The spectrum of the d-bar-Neumann Laplacian on a polydisc in several complex variables is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, s…
Hearing the type of a domain in C^2 with the d-bar-Neumann Laplacian
Siqi Fu
A smooth bounded pseudoconvex domain in two complex variables is of finite type if and only if the number of eigenvalues of the d-bar-Neumann Laplacian that are less than or equal…
Hearing pseudoconvexity with the Kohn Laplacian
Siqi Fu
A bounded domain in several complex variables with connected Lipschitz boundary is pseudoconvex if and only if the bottom of the (essential) spectrum of the Kohn Laplacian is posit…
Compactness in the d-bar Neumann problem, magnetic Schrodinger operators, and the Aharonov-Bohm effect
Michael Christ, Siqi Fu
Compactness of the d-bar Neumann operator is studied for weakly pseudoconvex bounded Hartogs domains in two dimensions. A nonsmooth example is constructed in which condition (P) fa…
Semi-classical analysis of Schrodinger operators and compactness in the d-bar-Neumann problem
Siqi Fu, Emil J. Straube
We study the asymptotic behavior, in a ``semi-classical limit'', of the first eigenvalues (i.e. the groundstate energies) of a class of Schrödinger operators with magnetic fields a…
Compactness in the d-bar-Neumann problem
Siqi Fu, Emil J. Straube
This paper surveys the theory of compactness of the d-bar-Neumann problem. It also contains several results which improve upon what was previously known.