¹Instituto de Cibernética Matemática y Física, La Habana, Cuba. Email: rdm@yahoo.com

En este trabajo se caracterizan las formas bilineales cuyos funcionales asociados anulen a los múltiplos de (x\overline{y}-1)²ⁿ⁺¹, primero cuando éstos son funcionales generales, posteriormente cuando éstos son hermíticos. También se caracterizan las sucesiones de momentos asociadas a estas formas bilineales y se presenta un análogo del teorema de Favard.

Palabras clave: Producto de Sobolev, teorema de Favard, sucesión de momentos..

In this work we characterize the bilinear forms whose associated functionals vanish the multiples of (x\overline{y}-1)²ⁿ⁺¹, n = 0, 1, ..., first when they are general functionals and later on when they are hermitian. Besides we characterize the sequences of moments associated to this bilinear forms and an analog of Favards Theorem is presented.

Key words: Sobolev's Product, Favard's theorem, sequence of moments..

Texto completo disponible en PDF

Referencias

[1] Barrios, D., Lopez, G. & Pijeira, H., `The moment problem for a Sobolev inner product´, J. Approx. Theory 100, (1999), 364-380.         [ Links ]

[2] Berriochoa, E. & Cachafeiro, A., `A family of Sobolev orthogonal polynomials on the unit circle´, J. Comput. Appl. Math. 105, (1999), 163-173.         [ Links ]

[3] Berriochoa, E. & Cachafeiro, A., `Strong asymptotics inside the unit circle for Sobolev orthogonal polynomials´, Comput. Math. and Appl. 44, (2002), 253-261.         [ Links ]

[4] Berriochoa, E. & Cachafeiro, A., `On the strong asymptotics for Sobolev orthogonal polynomials on the circle´, Const. Approx. 19, (2003), 299-307.         [ Links ]

[5] Duran, A., `A generalization of Favard's theorem for polynomials satisfying a recurrence relation´, J. Approx. Theory 74, (1993), 83-109.         [ Links ]

[6] Lopez, G. & Pijeira, H., `Zero location and n-th root asymptotics of Sobolev orthogonal polynomials´, J. Approx. Theory 99, (1999), 30-43.         [ Links ]

[7] Lopez, G., Pijeira, H. & Pérez, I., `Sobolev orthogonal polynomials in the complex plane´, J. Comput. Appl. Math. 127, (2001), 219-230.         [ Links ]

[8] Marcellán, F. & Alvarez-Nodarse, R., `On the ``Favard'' theorem and their extensions´, J. Comput. Appl. Math. 127, (2001), 231-254.         [ Links ]

[9] Marcellán, F. & Szafraniec, F., `The Sobolev-type moment problem´, Proc. Amer. Math. Soc 128, (2000), 2309-2317.         [ Links ]

[10] Marcellán, F. & Szafraniec, F., `A matrix algorithm towards solving the moment problem of Sobolev type´, Lin. Alg. and its Appl. 331, (2001), 155-164.         [ Links ]

[11] Pijeira, H., Teoría de momentos y propiedades asintóticas para polinomios ortogonales de Sobolev, Tesis Doctoral, Universidad Carlos III de Madrid, 1998.         [ Links ]

[12] Robert, L., General orthogonal polynomials, Master's Thesis, University of Havana, Cuba, 2001.         [ Links ]

[13] Robert, L. & Santiago, L., `On a class of Sobolev scalar products in the polynomials´, J. Approx. Theory 125, (2003a), 169-189.         [ Links ]

[14] Robert, L. & Santiago, L., `The finite section method for Hessenberg matrices´, J. Approx. Theory 123, (2003b), 69-88.         [ Links ]

[15] Shohat, J. & Tamarkin, J., The Problem of Moments, American Mathematical Society, Providence, RI, 1963.         [ Links ]

[16] Zagorodnyuk, S., `Analog of Favard's theorem for polynomials connected with difference equation of 4th orde´, Serdica Math. J. 27, (2001), 193-202.         [ Links ]

[17] Zagorodnyuk, S., `On the moment problem of discrete Sobolev type´, Ukrain. Math. Bull. 2, (2005), 345-360. (In Russian). 2 (2005), 351-367. (In English).         [ Links ]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX: