Abstract
In the present paper we consider a regular and hermitian functional u defined in the space of Laurent polynomials and we study the solutions T of the equation \((Z - \alpha )({Z^{ - 1}} - \overline \alpha )T = u\) for α ∈ – {0} If we fix a solution T we obtain the corresponding sequence of moments, characterize the regularity and we determine the expression for the sequence of monic orthogonal polynomials related to T. Finally we study the positive definite case, we obtain the relation between the associated measures and we apply these results to the functional u induced by the Lebesgue normalized measure on the unit circle.
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© 1994 Springer Science+Business Media Dordrecht
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Cachafeiro, A., Suárez, C. (1994). Inverse Problems: Rational Modifications. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_8
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DOI: https://doi.org/10.1007/978-94-011-0970-3_8
Publisher Name: Springer, Dordrecht
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