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Francisco Marcellán

Bio: Francisco Marcellán is an academic researcher from Charles III University of Madrid. The author has contributed to research in topics: Orthogonal polynomials & Classical orthogonal polynomials. The author has an hindex of 34, co-authored 317 publications receiving 4751 citations. Previous affiliations of Francisco Marcellán include Georgia Institute of Technology & Carlos III Health Institute.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors characterize the classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel) using the distributional differential equation D(φu)=ψu.
Abstract: We characterize the so-called classical orthogonal polynomials (Hermite, Laguerre, Jacobi, and Bessel) using the distributional differential equation D(φu)=ψu. This result is naturally not new. However, other characterizations of classical orthogonal polynomials can be obtained more easily from this approach. Moreover, three new properties are obtained.

139 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of finding the monic Jacobi matrix associated with the three canonical perturbations in terms of the so-called Jacobi matrices associated with a quasi-definite linear functional.

131 citations

Journal ArticleDOI
TL;DR: Sobolev orthogonal polynomials have been studied extensively in the past quarter-century as discussed by the authors, and the research in this field has sprawled into several directions and generates a plethora of publications.

120 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an introductory survey of orthogonal polynomials on Sobolev spaces and their applications in the analysis of spectral methods for partial differential equations.

96 citations


Cited by
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Posted Content
18 Dec 2005
TL;DR: In this paper, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed and orthogonality on the unit circle is not discussed.
Abstract: In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed Orthogonal polynomials on the unit circle are not discussed

5,648 citations

Book ChapterDOI
01 Jan 1998

1,532 citations

Book
19 Mar 2001
TL;DR: In this article, the authors considered the properties of orthogonal polynomials on the unit sphere, root systems and Coxeter groups, and the Summability of Orthogonal expansions.
Abstract: Preface to the second edition Preface to the first edition 1. Background 2. Orthogonal polynomials in two variables 3. General properties of orthogonal polynomials in several variables 4. Orthogonal polynomials on the unit sphere 5. Examples of orthogonal polynomials in several variables 6. Root systems and Coxeter groups 7. Spherical harmonics associated with reflection groups 8. Generalized classical orthogonal polynomials 9. Summability of orthogonal expansions 10. Orthogonal polynomials associated with symmetric groups 11. Orthogonal polynomials associated with octahedral groups and applications References Author index Symbol index Subject index.

1,026 citations