Spectral properties of the canonical solution operator to dbar

2006/12/13 by Friedrich Haslinger, Haslinger, Friedrich, Bernhard Lamel +1
Computer Science · Mathematics · #32W05 #47B38 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0612352

openalex publication_date 2006/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study boundedness, compactness, and Schatten-class membership of the canonical solution operator to dbar, restricted to (0,1)-forms with holomorphic coefficients, on L²(d mu) where mu is a measure with the property that the monomials form an orthogonal family in L² (d mu). The characterizations are formulated in terms of moment properties of mu. Our results generalize the results of the first author to several variables, contain some known results for several variables, and also cover new ground.

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