Rational approximation and Sobolev-type orthogonality

Journal of Approximation Theory - Tập 260 - Trang 105481 - 2020
Abel Díaz-González1, Héctor Pijeira-Cabrera1, Ignacio Pérez-Yzquierdo2
1Universidad Carlos III de Madrid, Spain
2Universidad Autónoma de Santo Domingo, Dominican Republic

Tài liệu tham khảo

Baratchart, 2009, Meromorphic approximations of complex Cauchy transforms with polar singularities, Mat. Sb., 200, 3 de la Calle Ysern, 2001, Convergence of multipoint Padé-type approximants, J. Approx. Theory, 109, 257, 10.1006/jath.2000.3537 Derevyagin, 2007, On the convergence of Padé approximants of generalized nevanlinna functions, Trans. Mosk. Mat. Obs., 68, 133 Gonchar, 1975, On the convergence of Padé approximants for some classes of meromorphic functions, Mat. Sb., 97, 607 Gonchar, 1989, 1 Gonchar, 1997, Hermite-Padé approximants for systems of Markov-type functions, Sb. Math., 188, 33, 10.1070/SM1997v188n05ABEH000225 Hille, 1982 López Lagomasino, 1985, vol. 1171, 309 López Lagomasino, 1995, Relative asymptotics for orthogonal polynomials with respect to a discrete Sobolev inner product, Constr. Approx., 11, 107, 10.1007/BF01294341 López Lagomasino, 2001, Sobolev orthogonal polynomials in the complex plane, J. Comput. Appl. Math., 127, 219, 10.1016/S0377-0427(00)00498-2 Marcellán, 2013, Bases of the space of solutions of some fourth-order linear difference equations: applications in rational approximation, J. Difference Equations Appl., 19, 1632, 10.1080/10236198.2013.769531 Marcellán, 2015, On Sobolev orthogonal polynomials, Expo. Math., 33, 308, 10.1016/j.exmath.2014.10.002 Martinez-Finkelshtein, 2001, Analytic properties of Sobolev orthogonal polynomials revisited, J. Comput. Appl. Math., 127, 255, 10.1016/S0377-0427(00)00499-4 Nevai, 1979 Nikishin, 1991, vol. 92 Rahman, 2002 Rakhmanov, 1977, Convergence of diagonal Padé approximants, Mat. Sb., 104, 271 Rakhmanov, 1977, On the asymptotics of the ratio of orthogonal polynomials, Mat. Sb., 103, 237 Rakhmanov, 1982, On the asymptotics of the ratio of orthogonal polynomials II, Mat. Sb., 118, 104 Shohat, 1934 Szegő, 1975, vol. 23 Van Assche, 1991, Orthogonal polynomials, associated polynomials and functions of the second kind, J. Comput. Appl. Math., 37, 237, 10.1016/0377-0427(91)90121-Y