On a moment problem associated with Chebyshev polynomials

Castillo, K.; Lamblém, Regina Litz; Ranga, A. Sri

doi:10.1016/j.amc.2012.03.039

Cited by 3 publications

(4 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, it is well known that Chebyshev polynomials can be applied in several fields of Mathematics, for example in Numerical Analysis and Combinatorics (see, for instance: [3,5,7,13,19,23,26,4] and references therein). We think that also the Lucas-Lehmer polynomials could be adapted to solve similar problems.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper we show some properties of these polynomials, in particular discussing the link among the Lucas-Lehmer polynomials and the Chebyshev polynomials of the first and second kind [2,12,22]. The Chebyshev polynomials are well-known and, although they have been known and studied for a long time, continue to play an important role in recent advances in many areas of mathematics such as Algebra, Numerical Analysis, Differential Equations and Number Theory (see, for instance: [1,3,5,7,10,13,19,23,26,4]) and new other properties of theirs continue to be discovered ([3, 7, 8, 11]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The class of Lucas-Lehmer polynomials

Vellucci¹,

Bersani²

2016

Preprint

View full text Add to dashboard Cite

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The class of Lucas-Lehmer polynomials

Vellucci¹,

Bersani²

2016

Preprint

View full text Add to dashboard Cite

show abstract

“…We refer to [2,4,5,12] for other contributions about some other kinds of perturbations of moment functionals. Proposition 1.…”

Section: A Perturbation On the Antidiagonal Of A Hankel Matrixmentioning

confidence: 99%

Perturbations on the antidiagonals of Hankel matrices

Castillo

Dimitrov

Garza

et al. 2013

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

abst ractGiven a strongly regular Hankel matrix, and its associated sequence of moments which defines a quasi definite moment linear functional, we study the perturbation of a fixed moment, i.e., a perturbation of one antidiagonal of the Hankel matrix. We define a linear functional whose action results in such a perturbation and establish necessary and suffi cient conditions in order to preserve the quasi definite character. A relation between the corresponding sequences of orthogonal polynomials is obtained, as well as the asymptotic behavior of their zeros. We also study the invariance of the Laguerre Hahn class of linear functionals under such perturbation, and determine its relation with the so called canon ical linear spectral transformations.

show abstract

“…Other fundamental properties, especially of an analytic nature, of polynomials * , * , * and * are presented in monographs [2,4], see also interesting new results on a moment problem [12].…”

Section: Introductionmentioning

confidence: 99%

A geometric property of the roots of Chebyshev polynomials

Wituła

Hetmaniok

Słota

2014

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

Abstract. In this text a new property of geometric nature of the Chebyshev polynomials is given. It is proven that the lengths of diagonals of a regular n-gon with the side of length equal to one are the sums of positive roots of the respective renormalized Chebyshev polynomials of one from among four types. Some new special decompositions of differences of values of the Chebyshev polynomials are also presented.

show abstract

On a moment problem associated with Chebyshev polynomials

Cited by 3 publications

References 6 publications

The class of Lucas-Lehmer polynomials

The class of Lucas-Lehmer polynomials

Perturbations on the antidiagonals of Hankel matrices

A geometric property of the roots of Chebyshev polynomials

Contact Info

Product

Resources

About