The Quasi-Canonical Solution Operator to
$${\bar \partial }$$
Restricted to the Fock-Space |
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Authors: | Georg Schneider |
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Institution: | (1) Institut fur Mathematik, Universitat Wien, Nordbergstr. 15, A-1090 Wien, Austria;(2) Present address: Institut fur Betriebswirtschaftslehre, Brunner Strasse 72, A-1210 Wien, Austria |
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Abstract: | We consider the solution operator S: ℱμ,(p,q) → L
2(μ)(p, q) to the
-operator restricted to forms with coefficients in ℱμ = {f: f is entire and ∫ℂn
|f(z)|2 dμ(z) < ∞}. Here ℱμ,(p,q) denotes (p,q)-forms with coefficients in ℱμ, L
2(μ) is the corresponding L
2-space and μ is a suitable rotation-invariant absolutely continuous finite measure. We will develop a general solution formula
S to
. This solution operator will have the property Sv ⊥ ℱ(p,q) ∀v ∈ ℱ(p,q+1). As an application of the solution formula we will be able to characterize compactness of the solution operator in terms
of compactness of commutators of Toeplitz-operators
: ℱμ → L
2(μ). |
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Keywords: | Fock-space Hankel-operator reproducing kernel |
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