On an inverse problem for a linear combination of orthogonal polynomials

References

• M.Alfaro, A.Peña, J.Petronilho, and M.L.Rezola, Orthogonal polynomials generated by a linear structure relation: Inverse problem, J. Math. Anal. Appl. 401(1) (2013), pp. 182–197.
   Web of Science ®Google Scholar
• M.Alfaro, A.Peña, M.L.Rezola, and F.Marcellán, Orthogonal polynomials associated with an inverse quadratic spectral transform, Comput. Math. Appl. 61 (2011), pp. 888–900.
   Web of Science ®Google Scholar
• M.Alfaro, F.Marcellán, A.Peña, and M.L.Rezola, On linearly related orthogonal polynomials and their functionals, J. Math. Anal. Appl. 287 (2003), pp. 307–319.
   Web of Science ®Google Scholar
• M.Alfaro, F.Marcellán, A.Peña, and M.L.Rezola, When do linear combinations of orthogonal polynomials yield new sequences of orthogonal polynomials? J. Comput. Appl. Math. 233 (2010), pp. 1446–1452.
   Web of Science ®Google Scholar
• A.Branquinho and F.Marcellán, Generating new classes of orthogonal polynomials, Int. J. Math. Math. Sci. 19 (1996), pp. 643–656.
   Google Scholar
• T.S.Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, NY, 1978.
   Google Scholar
• T.S.Chihara, On co-recursive orthogonal polynomials, Proc. Amer. Math. Soc. 8 (1957), pp. 899–905.
   Google Scholar
• M.N.de Jesus and J.Petronilho, On orthogonal polynomials obtained via polynomial mappings, J. Approx. Theory 162 (2010), pp. 2243–2277.
   Web of Science ®Google Scholar
• S.Elaydi, An Introduction to Difference Equations, Springer, New York, NY, 2005.
   Google Scholar
• W.Gautschi, Orthogonal Polynomials: Computation and Approximation, Numerical Mathematics and Scientific Computation. Oxford University Press, New York, NY, 2004.
   Google Scholar
• J.S.Geronimo and W.Van Assche, Orthogonal polynomials on several intervals via a polynomial mapping, Trans. Amer. Math. Soc. 308 (1988), pp. 559–581.
   Web of Science ®Google Scholar
• Ya. L.Geronimus, On some finite difference equations and corresponding systems of orthogonal polynomials, Mem. Math. Sect. Fac. Phys. Kharkov State Univ. Kharkov Math. Soc 25 (1975), pp. 81–100.
   Google Scholar
• Ya. L.Geronimus, Sur quelques équations aux différences finies et les systèmes correspondants des polynômes orthogonaux. C.R. (Dokl.), Acad. Sci. URSS 29 (1940), pp. 536–538.
   Google Scholar
• Z.Grinshpun, Special linear combinations of orthogonal polynomials, J. Math. Anal. Appl. 299(1) (2004), pp. 1–18.
   Web of Science ®Google Scholar
• R.Koekoek, P.A.Lesky, and R.F.Swarttouw, Hypergeometric orthogonal polynomials and their q-analogues. With a foreword by Tom H. Koornwinder, Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2010.
   Google Scholar
• F.Marcellán and J.Petronilho, Orthogonal polynomials and coherent pairs: The classical case, Indag. Math. (NS) 6 (1995), pp. 287–307.
   Web of Science ®Google Scholar
• P.Maroni and I.Nicolau, On the inverse problem of the product of a form by a polynomial: The cubic case, Appl. Numer. Math. 45(4) (2003), pp. 419–451.
   Web of Science ®Google Scholar
• P.Maroni, Semi-classical character and finite-type relations between polynomial sequences, Appl. Numer. Math. 31(3) (1999), pp. 295–330.
   Web of Science ®Google Scholar
• P.Maroni, Sur la suite de polynômes orthogonaux associée à la forme , Period. Math. Hungar. 21(3) (1990), pp. 223–248.
   Google Scholar
• P.Maroni, Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semi-classiques, in Orthogonal Polynomials and their Applications, IMACS Ann. Comput. Appl. Math. C.Brezinski, L.Gori, and A.Ronveaux, eds., Vol. 9, Baltzer, Basel, 1991, pp. 95–130.
   Google Scholar
• F.Peherstorfer, On Bernstein-Szegő orthogonal polynomials on several intervals. II. Orthogonal polynomials with periodic recurrence coefficients, J. Approx. Theory 64 (1991), pp. 123–161.
   Web of Science ®Google Scholar
• J.Petronilho, On the linear functionals associated to linearly related sequences of orthogonal polynomials, J. Math. Anal. Appl. 315 (2006), pp. 379–393.
   Web of Science ®Google Scholar
• V.B.Uvarov, The connection between systems of polynomials that are orthogonal with respect to different distribution functions, Comput. Math. Math. Phys. 9 (1969), pp. 25–36.
   Google Scholar
• A.Zhedanov, Rational spectral transformations and orthogonal polynomials, J. Comput. Appl. Math. 85 (1997), pp. 67–86.
   Web of Science ®Google Scholar