It is proved that the class of operator equations F(y) = f solvable by a DSM (dynamical systems method) Newton-type method, u̇ = −[F (u) + a(t)I]−1[Fu(t) + a(t)u − f ], u(0) = u0, (∗) is large. Here F : X → X is a continuously Fréchet differentiable operator in a Banach space X , a(t) : [0, ∞) → C is a function, limt→∞ |a(t)| = 0, and there exists a y ∈ X such that F(y) = f . Under weak assumpti...

The aim of this paper is to study the q-Schrödinger operator L = q(x) −∆q, where q(x) is a given function of x defined over R q = {qn, n ∈ Z} and ∆q is the q-Laplace operator ∆qf(x) = 1 x [ f(qx)− 1 + q q f(x) + 1 q f(qx) ]

Let φ be an analytic map of unit disk D into itself, consider the composition operator Cφ defined by Cφ(f) = f◦φ whenever f is analytic on D. In this paper, we discuss necessary and sufficient conditions under which a composition operator on a large class of weighted Hardy spaces is a compact.

The Orbit Problem consists of determining, given a linear transformation A on Q, together with vectors x and y, whether the orbit of x under repeated applications of A can ever reach y. This problem was famously shown to be decidable by Kannan and Lipton in the 1980s. In this paper, we are concerned with the problem of synthesising suitable invariants P ⊆ R, i.e., sets that are stable under A a...

Let R denote a domain in C with boundary B. Let X denote the closure of R. An operator T on a complex Hilbert space H has X as a spectral set if σ(T ) ⊂ X and ‖f(T )‖ ≤ ‖f‖R = sup{|f(z)| : z ∈ R} for every rational function f with poles off X. The expression f(T ) may be interpreted either in terms of the Riesz functional calculus, or simply by writing the rational function f as pq−1 for polyno...

I.1 Two short problems: 1. Suppose that (X,A, μ) is a measure space, and X = ∪j=1Xj with Xj ⊂ Xj+1 for all j. Let χj be the indicator (characteristic) function of Xj, and let Mj denote the multiplication operator by χj acting on Z = Lp(X, dμ), 1 ≤ p < ∞. Show that Mj → I, the identity operator, in the strong operator topology, i.e. the weakest topology on bounded linear operators L(Z) in which ...

This article present a parallel CPU implementation of Kannan algorithm for solving shortest vector problem in Block Korkin-Zolotarev lattice reduction method. Implementation based on Native POSIX Thread Library and show linear decrease of runtime from number of threads.

We prove that spectral projections of Laplace-Beltrami operator on the m-complex unit sphere E∆ S2m−1 ([0, R)) are uniformly bounded as an operator from H(S) to L(S) for all p ∈ (1,∞). We also show that the Bochner-Riesz conjecture is true when restricted to cylindrically symmetric functions on R × R. Suppose that L is a positive definite, self-adjoint operator acting on L(X,μ), where X is a me...

Connected morphological operators act o n the level of the f la t zones of a n image, i.e., the connected regions where the grey-level i s constant. For binary i m ages, the f la t zones are the foreground and background grains (connected components) of the image. T h e f lat zones constitute a partition of the underlying space. A connected operator is a n operator that makes this part i t ion ...