Let H∞(D) denote the algebra of bounded analytic functions on the open unit disc in the complex plane. For a function g ∈ L∞(D), the Hankel-type operator Sg is defined by Sg(f) = gf +H∞(D). We give here an overview of the study of the symbol of the Hankel-type operator, with emphasis on those symbols for which the operator is compact, weakly compact, or completely continuous. We conclude with a...

The aim of this paper is to present an algorithm for computing orthogonal polynomials. The Fast Fourier Transform completes the connection given by Draux between the three-term recurrence relationship and the Euclidian algorithm. Applications to Hankel systems and numerical examples illustrate our purpose.

We define a generalization of the Stirling numbers of the second kind, which depends on two parameters. The matrices of integers that result are exponential Riordan arrays. We explore links to orthogonal polynomials by studying the production matrices of these Riordan arrays. Generalized Bell numbers are also defined, again depending on two parameters, and we determine the Hankel transform of t...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

Abstract Tracy and Widom showed that fundamentally important kernels in random matrix theory arise from systems of differential equations with rational coefficients. More generally, this paper considers symmetric Hamiltonian systems and determines the properties of kernels that arise from them. The inverse spectral problem for self-adjoint Hankel operators gives sufficient conditions for a self...

We are going to give the example of the operator weight W satisfying operator Hunt-Muckenhoupt-Wheeden A 2 condition but which provides the unbounded martingale transform on L 2 (W). The construction relates weighted boundedness with the boundedness of \dyadic vector Hankel operators".