On some spectral properties of the weighted -?-Neumann operator

摘要

We study necessary conditions for compactness of the weighted ?-Neumann operator on the space L~2(C~n, e~(-Φ)) for a plurisubharmonic function Φ. Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, aweaker result is obtained by simpler methods.Moreover,we investigate (non)compactness of the ?-Neumann operator for decoupled weights, which are of the form Φ(z) = Φ1(z1) + · · · + Φn(zn). More can be said if every ΔΦj defines a nontrivial doubling measure.