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Description: |
In the framework of approximation theory, a Cohen type inequality is a lower bound for the norm of the partial sums of the Fourier expansions in terms of a certain orthogonal system. This kind of inequalities have been investigated by many authors in various contexts and forms, including the theory of orthogonal polynomials.
Even though Dreseler and Soardi seem to be the first who found Cohen type inequalities in the setting of Jacobi expansions, it is worthwhile to point out that is due to Markett the presentation of an approach admitting a simpler proof of Dreseler and Soardi result for Jacobi expansions and stating the corresponding Cohen type inequalities for Laguerre and Hermite expansions.
Concerning Sobolev orthogonality, the study of Cohen type inequalities is most recent and it has attracted considerable attention. Marcellán and Fejzullahu have obtained Cohen type inequalities for Laguerre orthonormal expansions with respect to discrete Sobolev inner products with only one mass point at c = 0.
In this talk we are going to establish a Cohen type inequality when we deal with a discrete Laguerre-Sobolev inner product with only a mass point c located outside the support of the measure. In order to do this, we will incorporate new test functions different from whose used in the works previously mentioned. Then, as an immediate consequence we will deduce the divergence of Fourier expansions and Cesàro means of order \delta in terms of this kind of Laguerre-Sobolev polynomials.
This is a joint work with E. Huertas, F. Marcellán and Y. Quintana.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
Maria Francisca Perez Valero (Univ. Carlos III, Madrid, Spain)
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Institution: |
Univ. Carlos III, Madrid, Spain
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Place: |
Sala 5.5
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| Research Groups: |
-Analysis
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See more:
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