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Results tagged with kernels
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user 153260
1
vote
Pair of positive harmonic functions with negative inner product in Drury-Arveson space
I will try to prove that such functions do not exist. Suppose that $f,g$ are positive (pluri)harmonic functions in the pluri harmonic Drury Arveson space $\mathcal{H}DA_d$ such that $ \langle f ,g \ra …
0
votes
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 transformat …
1
vote
Accepted
Orthonormal bases in RKHSs via interpolating sequences
It is true that if a sequence $(k_n)$ is interpolating for $M(\mathcal{H})$, then the normalized Kernel vectors $g_n:=K_{k_n}/\Vert K_{k_n} \Vert_\mathcal{H} $ form a Riesz system in $\mathcal{H}$. O …