Compactness for the d-bar - Neumann problem - a functional analysis approach

2009/12/22 by Friedrich Haslinger, Haslinger, Friedrich · 1 citation
Computer Science · Mathematics · #32A36 #32W05 #35J10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.0912.4406

openalex publication_date 2009/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss compactness of the d-bar-Neumann operator in the setting of weighted L²-spaces on Cⁿ. For this purpose we use a description of relatively compact subsets of L²- spaces. We also point out how to use this method to show that property (P) implies compactness for the d-bar-Neumann operator on a smoothly bounded pseudoconvex domain and mention an abstract functional analysis characterization of compactness of the d-bar-Neumann operator.

Cited by

• Compactness of the d-bar-Neumann operator on singular complex spaces

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