in this paper we establish several polynomials similar to bernstein's polynomials and several refinements of  hermite-hadamard inequality for convex functions.

In this paper we study some properties of tensor categories that arise in 2-dimensional conformal and 3-dimensional topological quantum field theory – so called modular tensor categories. By definition, these categories are braided tensor categories with duality which are semisimple, have finite number of simple objects and satisfy some non-degeneracy condition. Our main example of such a categ...

This paper is devoted to various considerations on a family of sharp interpolation inequalities on the sphere, which in dimension greater than 1 interpolate between Poincaré, logarithmic Sobolev and critical Sobolev (Onofri in dimension two) inequalities. The connection between optimal constants and spectral properties of the Laplace-Beltrami operator on the sphere is emphasized. The authors ad...

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals