Friedrich Haslinger
Compactness for the $\overline\partial$-Neumann problem - a Functional Analysis Approach
Preprint series: ESI preprints

MSC:

32F20 $\overline\partial$- and $\overline\partial_b$-Neumann problems, See also {35N15}

35N15 $\overline\partial$-Neumann problem and generalizations; formal complexes, See also {32F20 and 58G05}

32A37 Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA) in $n$ dimensions), See also {46Exx}

35J10 Schrodinger operator, See also {35Pxx}

Abstract: We discuss compactness of the $\ovprt $-Neumann operator in the setting of
weighted $L^2$-spaces on $\mathbb{C}^n.$
For this purpose we use a description of relatively compact subsets of $L^2$- spaces.
We also point out how to use this method to show that property (P) implies compactness
for the $\ovprt $-Neumannoperator on a smoothly bounded pseudoconvex domain and mention
an abstract functional analysis characterization of compactness of the $\ovprt $-Neumann operator.


Keywords: $\overline\partial$-Neumann problem, Sobolev spaces, compactness