RT Journal Article
T1 A canonical family of multiple orthogonal polynomials for Nikishin systems
A1 López Lagomasino, Guillermo
A1 Álvarez Rocha, Ignacio
AB For any pair of compact intervals Δ1 and Δ2 of the real line such that Δ1∩Δ2 = ø we obtain two pairs of absolutely continuous probability measures (μ1,μ2) and (τ1,τ2) supported on Δ1 and Δ2, respectively, such that:
AB - for appropriate constants C1 and C2, (μ1,μ2) is the Nikishin system generated by (μ1,C1τ1) and (τ1,τ2) the Nikishin system generated by (τ1,C2μ1),
AB - the polynomials of multiple orthogonality with respect to the Nikishin system(μ1,μ2) and indices {..., (n,n), (n+1,n), ...} satisfy a recurrence relations with constant coe±cients of period 2,
AB - 1/hat-μ1(z) and 1/hat-μ2(z) are the functions which describe the ratio asymptotics of multiple orthogonal polynomials with respect to an arbitrary Nikishin system N(σ1,σ2) verifying supp(σi) = Δi, and σi' > 0, i = 1,2, almost everywhere on Δi. Analogously,1/hat-τ1(z) and 1/hat-τ2(z) give the ratio asymptotics for N(σ1,σ2).
YR 2009
FD 2009-12
LK https://hdl.handle.net/10016/6394
UL https://hdl.handle.net/10016/6394
LA eng
NO 16 pages.-- MSC2000 codes: Primary 42C05, 33C25; Secondary 41A21.-- Submitted paper.
NO The research of both authors was supported by research grant MTM 2006-13000-C03-02 of Ministerio de Ciencia e Innovación, Spain. I.A. Rocha also received support from Universidad Politécnica de Madrid through Grupo de Investigación TACA.
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RD 8 ago. 2024