Abstract We establish the mean convergence for multiple ergodic averages with iterates given by distinct fractional powers of primes and related recurrence results. A consequence our main result is that every set integers positive upper density contains patterns form $\{m,m+[p_n^a], m+[p_n^b]\}$ , where $a,b$ are nonintegers $p_n$ denotes n th prime, a property fails if or b natural number. Our...

This paper studies the celebrated KuramotoSakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets n-torus called winding cells. Second, analyze semicontractivity model, i.e., property that distance between trajectories decreases when measured according to a seminorm. establishes local Kuramoto-Sakaguchi which is equivalent contractiv...

This paper is devoted to the maximal L1 regularity and asymptotic behavior for solutions inhomogeneous incompressible Navier-Stokes equations under a scaling-invariant smallness assumption on initial velocity. We obtain new global L1-in-time estimate Lipschitz seminorm of velocity field without any density fluctuation. In derivation this estimate, we study linear Stokes system with variable coe...

We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H div space. In order to keep the estimate sharp, a procedure for the minimization of the majorant term with respect to the ux variable...

This paper presents an abstract analysis of bounded variation (BV) methods for ill-posed operator equations Au = z. Let T(u) def = kAu ? zk 2 + J(u); where the penalty, or \regularization", parameter > 0 and the functional J(u) is the BV norm or seminorm of u, also known as the total variation of u. Under mild restrictions on the operator A and the functional J(u), it is shown that the function...

When discrete ill-posed problems are analyzed and solved by various numerical regularization techniques, a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector. In particular, the graph associated with Tikhonov regularization plays a central role. The main purpose of this paper is to advo...

We consider the nonlinear delay differential evolution equation { u′(t) ∈ Au(t)+ f (t, ut ), t ∈ R+, u(t) = g(u)(t), t ∈ [−τ, 0], where τ ≥ 0, X is a real Banach space, A is the infinitesimal generator of a nonlinear semigroup of contractions whose Lipschitz seminorm decays exponentially as t → e−ωt when t → +∞ and f : R+×C([−τ, 0]; D(A)) → X is jointly continuous. We prove that if f Lipschitz ...

Abstract. Let I be a finite interval and r, s ∈ N. Given a set M , of functions defined on I, denote by ∆+M the subset of all functions y ∈ M such that the s-difference ∆τ y(·) is nonnegative on I, ∀τ > 0. Further, denote by ∆+W r p , the class of functions x on I with the seminorm ‖x‖Lp ≤ 1, such that ∆τ x ≥ 0, τ > 0. Let Mn(hk) := Pn i=1 cihk(wit − θi) | ci, wi, θi ∈ R , be a single hidden la...

It is shown that a) it is possible to define the topology of any topological algebra by a collection of F -seminorms, b) every complete locally uniformly absorbent (complete locally A-pseudoconvex) Hausdorff algebra is topologically isomorphic to a projective limit of metrizable locally uniformly absorbent algebras (respectively, A-(k-normed) algebras, where k ∈ (0, 1] varies, c) every complete...

We consider the series expansion of [Formula: see text]-Hardy inequality [G. Barbatis, S. Filippas and A. Tertikas, Series for text] Hardy inequalities, Indiana Univ. Math. J. 52 (2003) 171–190], in particular case where distance is taken from an interior point a bounded domain text]. For we improve it by adding as remainder term optimally weighted critical Sobolev norm, generalizing result [S....