Geodesic
Orthogonal polynomials on rays: properties of zeros, related moment problems and symmetries
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 395-419 
S. M. Zagorodnyuk. Orthogonal polynomials on rays: properties of zeros, related moment problems and symmetries. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 395-419. http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We establish some basic properties of zeros for orthonormal polynomials on radial rays. We introduce a moment problem related to these orthonormal polynomials and obtain necessary and sufficient conditions for its solvability. We establish some properties of orthonormal polynomials in the case when the measure of orthogonality has symmetries and show that the moment problem has solutions with some symmetric properties.

[1] S. M. Zagorodnyuk, “On Generalized Jacobi Matrices and Orthogonal Polynomials”, New York J. Math., 9 (2003), 117–136 | MR | Zbl

[2] A. J. Duran, E. B. Saff, “Zero Location for Nonstandard Orthogonal Polynomials”, J. Approx. Th., 113 (2001), 127–141 | DOI | MR | Zbl

[3] G. Szegö, Orthogonal polynomials, AMS Colloquium Publ., XXIII, New York, 1959 | MR | Zbl

[4] P. K. Suetin, Classical Orthogonal Polynomials, Nauka, Moscow, 1979 (Russian) | MR | Zbl

[5] S. M. Zagorodnyuk, “On the Complex Moment Problem on Radial Rays”, J. Math. Phys., Anal., Geom., 1 (2005), 74–92 (Russian) | MR | Zbl

[6] S. M. Zagorodnyuk, “On the Moment Problem of Discrete Sobolev Type”, Ukr. Mat. Visn., 2:3 (2005), 345–361 (Russian) | MR | Zbl

[7] S. M. Zagorodnyuk, “On a Moments Problem on Rays in the Complex Plane”, Abstr. 2nd Int. Conf. “Math. Analysis and Economics” (Sumy, April 1–4), 2003, 58–59