Results 51 to 60 of about 1,174 (70)

Combinatorial polynomials as moments, Hankel transforms and exponential Riordan arrays [PDF]

arXiv, 2011
In the case of two combinatorial polynomials, we show that they can exhibited as moments of paramaterized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponential Riordan arrays are the main vehicles used for this.
arxiv  

Integrals Involving Associated Laguerre Polynomials [PDF]

arXiv, 2011
We present a closed-form expression for integrals involving product of associated Laguerre polynomials.
arxiv  

On the growth of the polynomial entropy integrals for the measures in the Szego class [PDF]

arXiv, 2011
For the polynomials orthogonal on the unit circle with respect to the measure from the Szego class we prove that the polynomial entropy integrals can grow. The estimate obtained is sharp.
arxiv  

On a conjecture for higher-order Szego theorems [PDF]

arXiv, 2012
We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.
arxiv  

Embedding structures associated with Riordan arrays and moment matrices [PDF]

arXiv, 2013
Every ordinary Riordan array contains two naturally embedded Riordan arrays. We explore this phenomenon, and we compare it to the situation for certain moment matrices of families of orthogonal polynomials.
arxiv  

Sobolev spaces associated with Jacobi expansions [PDF]

J. Math. Anal. Appl. 420 (2014), 1533-1551, 2013
We define and study Sobolev spaces associated with Jacobi expansions. We prove that these Sobolev spaces are isomorphic to Jacobi potential spaces. As a technical tool, we also show some approximation properties of Poisson-Jacobi integrals.
arxiv  

Constructing bispectral dual Hahn polynomials [PDF]

arXiv, 2014
Using the concept of $\mathcal{D}$-operator and the classical discrete family of dual Hahn, we construct orthogonal polynomials $(q_n)_n$ which are also eigenfunctions of higher order difference operators.
arxiv  

Spectral measures with arbitrary Hausdorff dimensions [PDF]

arXiv, 2014
In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.
arxiv  

Infinite J-matrices and a matrix moment problem [PDF]

Dokl. Akad. Nauk 69, nr. 2 (1949), 125-128, 2016
This is a translation of a paper that appeared (in Russian) in Dokl. Akad. Nauk SSSR 69, nr 2 (1949), 125-128.
arxiv  

Minkowski's question mark measure is UST--regular [PDF]

arXiv, 2016
We prove the recent conjecture that Minkowski's question mark measure is regular, in the sense of Ullman-Stahl-Totik.
arxiv