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Analysis of institutional authors

Garcia-Ardila, JcCorresponding Author

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June 6, 2022
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Associated orthogonal polynomials of the first kind and Darboux transformations

Publicated to: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 508 (2): 125883- - 2022-04-15 508(2), DOI: https://doi.org/10.1016/j.jmaa.2021.125883

Authors:

Garcia-Ardila, JC; Marcellan, F; Villamil-Hernandez, PH
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Affiliations

Teoría de Aproximación Constructiva y Aplicaciones. Universidad Politécnica de Madrid - Author
Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Leganes 28911, Spain - Author
Univ Nacl Autonoma Mexico, Dept Metodos Matematicos & Numer, Inst Invest Matemat Aplicadas & Sistemas, Ciudad Univ, Ciudad De Mexico 04510, Mexico - Author
Univ Politecn Madrid, Dept Matemat Aplicada Ingn Ind, Calle Jose Gutierrez Abascal 2, Madrid 28006, Spain - Author
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Abstract

Let u be a quasi-definite linear functional defined on the linear space of polynomials P with complex coefficients. For such a functional we can define a sequence of monic orthogonal polynomials (SMOP in short) (P-n)(n is an element of N), which satisfies a three term recurrence relation. If we increase the indices of the recurrence relation by one unity, then we get the sequence of associated polynomials of the first kind as solution. These polynomials will be orthogonal with respect to a linear functional denoted by u((1)). In the literature two special transformations of the functional u are studied, the canonical Christoffel transformation (u) over slide & nbsp; = (x - c)u and the canonical Geronimus transformation (A) over tilde & nbsp; = (x - c)(-1)u + M delta(c), where c is a fixed complex number, M is a free complex parameter and delta c is the linear functional defined on P as (delta(c,) p(x)) = p(c). For the Christoffel transformation with SMOP ( P-n)n is an element of N, we are interested in analyzing the relation between the linear functionals u(1) and (u)oc=ver slide((1).) The super index denotes the linear functionals associated with the orthogonal polynomial sequences of the first kind (P-n(1))n is an element of N and ((P) over slide(n)((1)) )(n is an element of N), respectively. This problem is also studied for Geronimus transformations. Here we give close relations between their corresponding monic Jacobi matrices by using the LU and UL factorizations. To get this result, we first need to study the relation between u(-1) (the inverse functional) and u((1)) which can be given from a quadratic Geronimus transformation. (C)& nbsp;2021 Elsevier Inc. All rights reserved.& nbsp;
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Keywords

Darboux transformationsFirst kind orthogonal polynomialsFormFunctionalsInverse problemLaguerreLuLu, ul and qr factorizationProductUl and qr factorization

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2022, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category Analysis.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 3.38. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 13, 2025)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 1.96 (source consulted: FECYT Mar 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2026-04-26, the following number of citations:

  • WoS: 9
  • Scopus: 9
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-26:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/85279/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 133
  • Downloads: 2
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Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Mexico.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (GARCIA ARDILA, JUAN CARLOS) .

the author responsible for correspondence tasks has been GARCIA ARDILA, JUAN CARLOS.

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Awards linked to the item

We thank the suggestions and comments by the referees. They have contributed to improve the presentation of the manuscript. The work of the second author (FM) has been supported by FEDER/Ministerio de Ciencia e Innovacion-Agencia Estatal de Investigacion of Spain, grant PGC2018-096504-B-C33, and the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, grant EPUC3M23 in the context of the V PRICIT (Regional Programme of Research and Technological Innovation) .
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