Symmetric Measures and Associated Orthogonal Polynomials Obtained from Modified Positive Chain Sequences
Resumo
Given a nontrivial positive measure φ (i.e., a Borel measure with infinite support), we say that {Pn (x)}∞ n=0 is the sequence of monic orthogonal polynomials on the real line (MOPRL, in short) associated with φ, if Pn (x) is a monic polynomial of degree n satisfying xj Pn (x)dφ(x) = δn,j ρn , 0 ≤ j ≤ n, (1) R where δn,j is the Kronecker delta and ρn ̸= 0 for n ≥ 0. [...]
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Referências
T. S. Chihara. An Introduction to Orthogonal Polynomials. Mathematics and its Applications Series. Gordon and Breach, 1978. isbn: 978-0-677-04150-6.
M. E. H. Ismail. Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Application. Cambridge Univ. Press, 2005. isbn: 978-0-521-78201-2.
T. S. Chihara. “Chain Sequences and Orthogonal Polynomials”. In: Transactions of the American Mathematical Society 104 (1962), pp. 1–16. doi: 10.2307/1993928.
M. S. Costa, H. M. Felix, and A. Sri Ranga. “Orthogonal polynomials on the unit circle and chain sequences”. In: Journal of Approximation Theory 173 (2013), pp. 1–20. doi:10.1016/j.jat.2013.04.009.
D. O. Veronese. “Orthogonal Polynomials and Quadrature Rules on the Unit Circle Associated with Perturbations of Symmetric Measures”. In: Journal of Computational and Applied Mathematics 375 (2020), pp. 1–20. doi: 10.1016/j.cam.2020.112808.
