scholarly journals Small eigenvalues of large Hankel matrices: The indeterminate case

2002 ◽  
Vol 91 (1) ◽  
pp. 67 ◽  
Author(s):  
Christian Berg ◽  
Yang Chen ◽  
Mourad E. H. Ismail
Keyword(s):  
Lower Bound ◽  
Positive Constant ◽  
Moment Problems ◽  
Hankel Matrices ◽  
Orthonormal Polynomials ◽  
Indeterminate Moment Problems ◽  
Explicit Lower Bound ◽  
Indeterminate Case ◽  
Bounded Below ◽  
Small Eigenvalues

In this paper we characterize the indeterminate case by the eigenvalues of the Hankel matrices being bounded below by a strictly positive constant. An explicit lower bound is given in terms of the orthonormal polynomials and we find expressions for this lower bound in a number of indeterminate moment problems.

Errata: Small Eigenvalues of Large Hankel Matrices

1968 ◽  
Vol 19 (6) ◽  
pp. 1508
Author(s):  
Harold Widom ◽  
Herbert Wilf
Keyword(s):  
Hankel Matrices ◽  
Small Eigenvalues

scholarly journals Badly approximable points on self-affine sponges and the lower Assouad dimension

2017 ◽  
Vol 39 (3) ◽  
pp. 638-657 ◽  
Author(s):  
TUSHAR DAS ◽  
LIOR FISHMAN ◽  
DAVID SIMMONS ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Lower Bound ◽  
Hausdorff Dimension ◽  
Diophantine Approximation ◽  
Assouad Dimension ◽  
Badly Approximable Points ◽  
Bounded Below ◽  
Badly Approximable ◽  
Sierpinski Sponges

We highlight a connection between Diophantine approximation and the lower Assouad dimension by using information about the latter to show that the Hausdorff dimension of the set of badly approximable points that lie in certain non-conformal fractals, known as self-affine sponges, is bounded below by the dynamical dimension of these fractals. For self-affine sponges with equal Hausdorff and dynamical dimensions, the set of badly approximable points has full Hausdorff dimension in the sponge. Our results, which are the first to advance beyond the conformal setting, encompass both the case of Sierpiński sponges/carpets (also known as Bedford–McMullen sponges/carpets) and the case of Barański carpets. We use the fact that the lower Assouad dimension of a hyperplane diffuse set constitutes a lower bound for the Hausdorff dimension of the set of badly approximable points in that set.

On the infimum of the spectrum of a relativistic Schrödinger operator

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Mohammed El Aïdi
Keyword(s):  
Lower Bound ◽  
Euclidean Space ◽  
Schrödinger Operator ◽  
Schrodinger Operator ◽  
Relativistic Schrödinger Operator ◽  
Explicit Lower Bound

AbstractIn this paper, we look for an explicit lower bound of the smallest value of the spectrum for a relativistic Schrödinger operator in a domain of the Euclidean space.

An explicit lower bound for special values of Dirichlet L-functions

2018 ◽  
Vol 189 ◽  
pp. 272-303 ◽  
Author(s):  
Dongho Byeon ◽  
Jigu Kim
Keyword(s):  
Lower Bound ◽  
Special Values ◽  
Explicit Lower Bound

scholarly journals A question by T. S. Chihara about shell polynomials and indeterminate moment problems

2011 ◽  
Vol 163 (10) ◽  
pp. 1449-1464
Author(s):  
Christian Berg ◽  
Jacob Stordal Christiansen
Keyword(s):  
Moment Problems ◽  
Indeterminate Moment Problems

scholarly journals The discrete Kramer sampling theorem and indeterminate moment problems

2001 ◽  
Vol 134 (1-2) ◽  
pp. 13-22 ◽  
Author(s):  
Antonio G. Garcı́a ◽  
Miguel A. Hernández-Medina
Keyword(s):  
Sampling Theorem ◽  
Moment Problems ◽  
Indeterminate Moment Problems

scholarly journals On Proinov’s Lower Bound for the Diaphony

2020 ◽  
Vol 15 (2) ◽  
pp. 39-72
Author(s):  
Nathan Kirk
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Lower Bounds ◽  
Unit Cube ◽  
Integral Approximation ◽  
Quantitative Theory ◽  
Dimensional Unit ◽  
Explicit Lower Bound ◽  
Irregularities Of Distribution ◽  
Infinite Sequences

AbstractIn 1986, Proinov published an explicit lower bound for the diaphony of finite and infinite sequences of points contained in the d−dimensional unit cube [Proinov, P. D.:On irregularities of distribution, C. R. Acad. Bulgare Sci. 39 (1986), no. 9, 31–34]. However, his widely cited paper does not contain the proof of this result but simply states that this will appear elsewhere. To the best of our knowledge, this proof was so far only available in a monograph of Proinov written in Bulgarian [Proinov, P. D.: Quantitative Theory of Uniform Distribution and Integral Approximation, University of Plovdiv, Bulgaria (2000)]. The first contribution of our paper is to give a self contained version of Proinov’s proof in English. Along the way, we improve the explicit asymptotic constants implementing recent, and corrected results of [Hinrichs, A.—Markhasin, L.: On lower bounds for the ℒ2-discrepancy, J. Complexity 27 (2011), 127–132.] and [Hinrichs, A.—Larcher, G.: An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77]. (The corrections are due to a note in [Hinrichs, A.—Larcher, G. An improved lower bound for the ℒ2-discrepancy, J. Complexity 34 (2016), 68–77].) Finally, as a main result, we use the method of Proinov to derive an explicit lower bound for the dyadic diaphony of finite and infinite sequences in a similar fashion.

An explicit lower bound for special values of Dirichlet L-functions II

2019 ◽  
Vol 205 ◽  
pp. 194-209 ◽  
Author(s):  
Dongho Byeon ◽  
Jigu Kim
Keyword(s):  
Lower Bound ◽  
Special Values ◽  
Explicit Lower Bound
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