Abstract
Some types of Hermitian and positive definite matrices whose elements satisfy a linear recurrence relation have been studied in connection with the theory of orthogonal polynomials on algebraic curves; more precisely, for the lemniscates ([1]) and harmonic algebraic curves.
Through a linear recurrence relation for the moments of a Gram matrix, a necessary and sufficient condition for the extension is obtained. We obtain the moments in terms of a family of parameters, generalising the one’s introduced by Geronimus for the unit circle [4].
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© 1988 D. Reidel Publishing Company
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Marcellán, F., Pérez-Grasa, I. (1988). The Moment Problem on Equipotential Curves. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation. Mathematics and Its Applications, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2901-2_13
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DOI: https://doi.org/10.1007/978-94-009-2901-2_13
Publisher Name: Springer, Dordrecht
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