Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kerne...

We consider functions f of two real variables, given as trigonometric functions over a finite set F of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle 2kπ M for some integer M . Firstly, we address the problem of evaluating these functions over a similar finite set E in the space plane and, secondly, we address the problems of interpolating or appro...

We are interested in finding the sufficient conditions on A , B , λ , b and c which ensure that the generalized Bessel functions uλ := uλ ,b,c satisfies the subordination uλ (z) ≺ (1+Az)/(1+Bz) . Also, conditions for which uλ (z) to be Janowski convex, and zuλ (z) to be Janowski starlike in the unit disk D = {z ∈ C : |z| < 1} are obtained. Mathematics subject classification (2010): 34B30, 33C10...

In this paper, we treat a convolution-type operator called the generalized Bessel potential. Our main result is derivation of two different forms its inversion. The first inversion provided in terms an approximative inverse using method improving multiplier. second one employs regularization technique for divergent integrals form appropriate segments Taylor–Delsarte series.