We study syndetic sensitivity and mean for linear dynamical systems. For the aspect, we obtain some properties of adjoint operators left multiplication operators. also show that there exists a system (X×Y,T×S) such is cofinitely sensitive but (X,T) (Y,S) are not syndetically sensitive. if sensitive, where Y complex Banach space, spectrum T meets unit circle. results regarding perturbations.

This tutorial gives an introductive presentation of algebraic and geometric methods for solving a polynomial system f1 = · · · = fm = 0. The first class of methods is based on the study of the quotient algebra A of the polynomial ring modulo the ideal I = (f1, . . . , fm). We show how to deduce the geometry of the solutions, from the structure of A and in particular, how solving polynomial equa...

We introduce an algebra H consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of Sahi's double affine Hecke algebra related to the affine root system of type (C ∨ 1 , C1). We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra H, and the corresponding Fourier transforms. These eigenfunctions are non-symmetric v...