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Hernández-Medina MAuthor

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November 7, 2019
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Knit Product of Finite Groups and Sampling

Publicated to: Mediterranean Journal of Mathematics. 16 (6): 146- - 2019-12-01 16(6), DOI: 10.1007/s00009-019-1417-8

Authors:

García, AG; Hernández-Medina, MA; Ibort, A
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Affiliations

Univ Carlos III Madrid, Dept Matemat, Avda Univ 30, Leganes 28911, Spain - Author
Univ Politecn Madrid, Informat Proc & Telecommun Ctr, ETSIT, Dept Matemat Aplicada Tecnol Informat & Comunicac, Avda Complutense 30, E-28040 Madrid, Spain - Author
Universidad Carlos III de Madrid - Author
Universidad Politécnica de Madrid - Author
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Abstract

© 2019, Springer Nature Switzerland AG. A finite sampling theory associated with a unitary representation of a finite non-abelian group G on a Hilbert space is established. The non-abelian group G is a knit product N⋈ H of two finite subgroups N and H where at least N or H is abelian. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space ℓ2(G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results.
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Keywords

Dual framesFinite framesFinite unitary-invariant subspacesKnit product of groupsLeft-inversesPseudoinverseSampling expansionsUnitary representation of a group

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Mediterranean Journal of Mathematics due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2019, it was in position 79/325, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-25:

  • Google Scholar: 2
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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 2026-04-25:

  • 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: 5 (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:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/64003/

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: 362
  • Downloads: 197
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