Perturbations in Müntz's theorem

Singular Perturbations and a Theorem of Kisyriski*

where t > 0, E > 0 is a small parameter, and A is a nonnegative self-adjoint (not necessarily bounded) operator in H, converge, as E + 0, to the solution of (1.2). While we borrow Kisynski’s idea of using the functional calculus of the operator A in order to construct a solution of (1.3), our approach is different from Kisynski’s in that we do not employ the techniques of the theory of semigrou...

The Central Limit Theorem for Random Perturbations of Rotations

We prove a functional central limit theorem for stationary random sequences given by the transformations T ;! (x; y) = (2x; y + ! + x) mod 1 on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale diierences with values in a separable Hilbert space of square integrable functions.

Local Perturbations of Energy and Kac’s Return Time Theorem

A bstract. We introduce the notion of local perturbations for normalized energies and study their effect on the level of equilibrium measures. Using coupling technics and Kac’s return time theorem, we obtain some d̄-estimates for the equilibrium measures. These reveal stability of certain energies under local perturbations. They also show how some weak-⋆ convergence of equilibrium may be obtaine...

Sharkovskĭi Theorem for Multidimensional Perturbations of One-dimensional Maps Ii

We present a multidimensional generalization of the Sharkovskĭı Theorem concerning the appearance of periodic points for the self-maps on the real line. Introduction Let f : X → X be a map. We say that x ∈ X is a periodic point of period n if f(x) = x and f(x) 6= x for k = 1, . . . , n− 1. We begin with recalling the Sharkovskĭı Theorem. Theorem 1. Let the ordering of positive integers be as fo...

Sensitivity in ranking for perturbations of data in DEA