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Polynomial Counterexamples to Shanks' Conjecture in Dirichlet-Type Spaces over the Bidisc
We study optimal polynomial approximants in spaces of Dirichlet-type over the bidisc. Given a nonzero function f, the linear optimal polynomial approximant (opa) to its reciprocal is the affine polynomial p for which pf is closest to the constant function 1 in the space norm. We prove that, for ever
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