Abstract. We find a local (d + 1)× (d + 1) Riemann-Hilbert problem characterizing the skew-orthogonal polynomials associated to the partition function of the Gaussian Orthogonal Ensemble of random matrices with a potential function of degree d. Our Riemann-Hilbert problem is similar to a local d × d RiemannHilbert problem found by Kuijlaars and McLaughlin characterizing the bi-orthogonal polyno...

Convexity properties are often useful in characterizing and nding bounds for special function and their zeros, as well as in questions concerning the existence and uniqueness of zeros in certain intervals. In this survey paper, we describe some work related to the gamma function, the q-gamma function, Bessel and cylinder functions and the Hermite function.

The construction of a Lyapunov function characterizing the pullback attraction of a cocycle attractor of a nonautonomous discrete time dynamical system involving Lipschitz continuous mappings is presented.

We study approximation by arbitrary linear combinations of $n$ translates a single function periodic functions. construct some methods this for univariate functions in the class induced convolution with function, and prove upper bounds $L^p$-approximation convergence rate these methods, when $n \to \infty$, $1 \leq p \infty$. also generalize results to classes multivariate defined tensor produc...