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Results tagged with several-complex-variables
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user 153260
1
vote
Accepted
Equivalent condition for the Pick matrix being positive semidefinite
About your first question this is exactly the positivity of the determinant of the Pick matrix.
That is because if $\lambda_1,\lambda_2 \in \mathbb{D}$ then
\begin{align*} \det(P) & = \begin{bmatrix} …
3
votes
Accepted
Example of an $H^1$ function on the bidisk that is not a product of two $H^2$ functions
I asked the polydisc experts for a reference and in fact it is known. It was proved by by J.P. Rosay in this paper. It is in french but it shouldn't be difficult to understand.