We discuss problems on Hankel determinants and the classical moment problem related to and inspired by certain Vandermonde determinants for polynomial interpolation on (quadratic) algebraic curves in ℂ².
We introduce and study the notion of Taylorian points of algebraic curves in , which enables us to define intrinsic Taylor interpolation polynomials on curves. These polynomials in turn lead to the construction of a well-behaved Hermitian scheme on curves, of which we give several examples. We show that such Hermitian schemes can be collected to obtain Hermitian bivariate polynomial interpolation schemes.
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