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Results of invertibility of a matrix involving the Szego kernel

Expand the determinant $D=\det k(x_j,y_k)$ along the first row. This shows that as a function of $x=x_1$, it is of the form $$ D(x) = \sum_{j=1}^n \frac{c_j}{1-y_j x} , $$ with $c_j$ independent of $x=...
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Results of invertibility of a matrix involving the Szego kernel

Sorry for my previous answer. This is a partial answer for the $2\times 2$ case. Notice first that we can assume without loss of generality that $z_1=0$. Otherwise we can apply the Moebius ...
an_ordinary_mathematician's user avatar

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