Search results for "Linear"

Bivariate Grüss-Type Inequalities for Positive Linear Operators

2018

Univariate Grüss- and Ostrowski-Type Inequalities for Positive Linear Operators

2018

Completely positive invariant conjugate-bilinear maps on partial *-algebras

2007

The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of commutative, locally convex quasi*-algebras are also discussed.

New degeneration of Fay's identity and its application to integrable systems

2011

In this paper, we find a new degenerated version of Fay's trisecant identity; this degeneration corresponds to the limit when the four points entering the trisecant identity coincide pairwise. This degenerated version of Fay's identity is used to construct algebro-geometric solutions to the multi-component nonlinear Schrodinger equation. This identity also leads to an independent derivation of algebro-geometric solutions to the Davey–Stewartson equations previously obtained in [17] in the framework of the Krichever scheme. We also give the condition of smoothness of the obtained solutions.

Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem

2015

International audience; The purpose of this paper is to push forward the theory of operator-valued Riemann-Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method a la Deift-Zhou. In this paper, we demonstrate that the operator-valued Riemann-Hilbert problem arising in the characterization of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.

The KAM Theorem

2016

This theorem guarantees that, under certain assumptions, in the case of a perturbation \(\varepsilon H_{1}(\boldsymbol{J},\boldsymbol{\theta })\) with small enough ɛ, the iterated series for the generator W(θ i 0, J i ) converges (according to Newton’s procedure) and thus the invariant tori are not destroyed. The KAM theorem is valid for systems with two and more degrees of freedom. However, in the following, we shall deal exclusively with the case of two degrees of freedom.

A Kato's second type representation theorem for solvable sesquilinear forms

2017

Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established.

Nonlinear balayage on metric spaces

2009

We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage. Original Publication:Anders Björn, Jana Björn, Tero Mäkäläinen and Mikko Parviainen, Nonlinear balayage on metric spaces, 2009, Nonlinear Analysis, (71), 5-6, 2153-2171.http://dx.doi.org/10.1016/j.na.2009.01.051Copyright: Elsevier Science B.V., Amsterdam.http://www.elsevier.com/

Hasse diagrams and orbit class spaces

2011

Abstract Let X be a topological space and G be a group of homeomorphisms of X. Let G ˜ be an equivalence relation on X defined by x G ˜ y if the closure of the G-orbit of x is equal to the closure of the G-orbit of y. The quotient space X / G ˜ is called the orbit class space and is endowed with the natural order inherited from the inclusion order of the closure of the classes, so that, if such a space is finite, one can associate with it a Hasse diagram. We show that the converse is also true: any finite Hasse diagram can be realized as the Hasse diagram of an orbit class space built from a dynamical system ( X , G ) where X is a compact space and G is a finitely generated group of homeomo…

Nonlinear scalar field equations with general nonlinearity

2018

Consider the nonlinear scalar field equation \begin{equation} \label{a1} -\Delta{u}= f(u)\quad\text{in}~\mathbb{R}^N,\qquad u\in H^1(\mathbb{R}^N), \end{equation} where $N\geq3$ and $f$ satisfies the general Berestycki-Lions conditions. We are interested in the existence of positive ground states, of nonradial solutions and in the multiplicity of radial and nonradial solutions. Very recently Mederski [30] made a major advance in that direction through the development, in an abstract setting, of a new critical point theory for constrained functionals. In this paper we propose an alternative, more elementary approach, which permits to recover Mederski's results on the scalar field equation. T…