- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 307974, 8 pages
-Coherent Pairs on the Unit Circle
1Facultad de Ciencias, Universidad de Colima, Bernal Díaz del Castillo 340, 28045 Colima, COL, Mexico
2Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Spain
Received 23 July 2013; Accepted 19 September 2013
Academic Editor: Jinde Cao
Copyright © 2013 Luis Garza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. Iserles, P. E. Koch, S. P. Nørsett, and J. M. Sanz-Serna, “On polynomials orthogonal with respect to certain Sobolev inner products,” Journal of Approximation Theory, vol. 65, no. 2, pp. 151–175, 1991.
- A. M. Delgado and F. Marcellán, “Companion linear functionals and Sobolev inner products: a case study,” Methods and Applications of Analysis, vol. 11, no. 2, pp. 237–266, 2004.
- H. G. Meijer, “Determination of all coherent pairs,” Journal of Approximation Theory, vol. 89, no. 3, pp. 321–343, 1997.
- M. N. de Jesus, F. Marcellán, J. Petronilho, and N. C. Pinzón-Cortés, “-coherent pairs of order and Sobolev orthogonal polynomials,” Journal of Computational and Applied Mathematics, vol. 256, pp. 16–35, 2014.
- M. N. de Jesus and J. Petronilho, “On linearly related sequences of derivatives of orthogonal polynomials,” Journal of Mathematical Analysis and Applications, vol. 347, no. 2, pp. 482–492, 2008.
- M. N. de Jesus and J. Petronilho, “Sobolev orthogonal polynomials and -coherent pairs of measures,” Journal of Computational and Applied Mathematics, vol. 237, no. 1, pp. 83–101, 2013.
- F. Marcellán and N. C. Pinzón-Cortés, “Higher order coherent pairs,” Acta Applicandae Mathematicae, vol. 121, pp. 105–135, 2012.
- I. Area, E. Godoy, and F. Marcellán, “Classification of all -coherent pairs,” Integral Transforms and Special Functions, vol. 9, no. 1, pp. 1–18, 2000.
- I. Area, E. Godoy, and F. Marcellán, “-coherent pairs and -orthogonal polynomials,” Applied Mathematics and Computation, vol. 128, no. 2-3, pp. 191–216, 2002.
- I. Area, E. Godoy, and F. Marcellán, “-coherent pairs and orthogonal polynomials of a discrete variable,” Integral Transforms and Special Functions, vol. 14, no. 1, pp. 31–57, 2003.
- F. Marcellán and N. C. Pinzón-Cortés, “(1,1)--coherent pairs,” Journal of Difference Equations and Applications, 2013.
- F. Marcellán and N. C. Pinzón-Cortés, “--coherent pairs,” Numerical Algorithms, vol. 60, no. 2, pp. 223–239, 2012.
- R. Álvarez-Nodarse, J. Petronilho, N. C. Pinzón-Cortés, and R. Sevinik-Adgüzel, “On linearly related sequences of difference derivatives of discrete orthogonal polynomials,” in progress.
- A. Branquinho, A. F. Moreno, F. Marcellán, and M. N. Rebocho, “Coherent pairs of linear functionals on the unit circle,” Journal of Approximation Theory, vol. 153, no. 1, pp. 122–137, 2008.
- A. Branquinho and M. N. Rebocho, “Structure relations for orthogonal polynomials on the unit circle,” Linear Algebra and Its Applications, vol. 436, no. 11, pp. 4296–4310, 2012.
- Ya. L. Geronimus, Orthogonal Polynomials: Estimates, Asymptotic Formulas, and Series of Polynomials Orthogonal on the Unit Circle and on an Interval, vol. 18, Consultants Bureau, New York, NY, USA, 1961.
- Ya. L. Geronimus, Polynomials Orthogonal on a Circle and Their Applications, vol. 3 of American Mathematical Society Translations, Providence, RI, USA, 1962.
- G. Szegő, Orthogonal Polynomials, vol. 23 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 4th edition, 1975.
- B. Simon, Orthogonal Polynomials on the Unit Circle, vol. 54 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 2005.
- A. Máté and P. G. Nevai, “Remarks on E. A. Rakhmanov's paper: “The asymptotic behavior of the ratio of orthogonal polynomials”,” Journal of Approximation Theory, vol. 36, no. 1, pp. 64–72, 1982.
- A. Máté, P. Nevai, and V. Totik, “Extensions of Szegő's theory of orthogonal polynomials. II,” Constructive Approximation, vol. 3, no. 1, p. 51–72, 73–96, 1987.
- F. Peherstorfer and R. Steinbauer, “Characterization of orthogonal polynomials with respect to a functional,” Journal of Computational and Applied Mathematics, vol. 65, no. 1–3, pp. 339–355, 1995.
- K. Castillo, L. Garza, and F. Marcellán, “Linear spectral transformations, Hessenberg matrices, and orthogonal polynomials,” Rendiconti Circolo Matematico di Palermo, vol. 2, supplement 82, pp. 3–26, 2010.
- F. Peherstorfer, “A special class of polynomials orthogonal on the unit circle including the associated polynomials,” Constructive Approximation, vol. 12, no. 2, pp. 161–185, 1996.