Weighted generalization of the Szegö kernel and how it can be used to prove general theorems of complex analysis
We consider weighted generalization of the Szegö kernel. We show which conditions must a weight of integration satisfy in order for weighted Szegö kernel to exist. Then we show some properties of weighted Szegö kernel, including a direct formula for particular cases. At the end, we show how weighted Szegö kernel can be used to prove general theorems of complex analysis.
KeywordsReproducing kernel Hilbert space Szegö kernel.
Mathematics Subject Classification (2000)32A25 46E22.
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