Search results for "predicate"

Weak commutation relations of unbounded operators: Nonlinear extensions

2013

We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.

A New Extension of Darbo's Fixed Point Theorem Using Relatively Meir-Keeler Condensing Operators

2018

We consider relatively Meir–Keeler condensing operators to study the existence of best proximity points (pairs) by using the notion of measure of noncompactness, and extend a result of Aghajani et al. [‘Fixed point theorems for Meir–Keeler condensing operators via measure of noncompactness’, Acta Math. Sci. Ser. B35 (2015), 552–566]. As an application of our main result, we investigate the existence of an optimal solution for a system of integrodifferential equations.

Jeu de taquin and diamond cone for Lie (super)algebras

2015

Abstract In this paper, we recall combinatorial basis for shape and reduced shape algebras of the Lie algebras gl ( n ) , sp ( 2 n ) and so ( 2 n + 1 ) . They are given by semistandard and quasistandard tableaux. Then we generalize these constructions to the case of the Lie superalgebra spo ( 2 n , 2 m + 1 ) . The main tool is an extension of Schutzenberger's jeu de taquin to these algebras.

Weyl's Theorems and Extensions of Bounded Linear Operators

2012

A bounded operator $T\in L(X)$, $X$ a Banach space, is said to satisfy Weyl's theorem if the set of all spectral points that do not belong to the Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues and having finite multiplicity. In this article we give sufficient conditions for which Weyl's theorem for an extension $\overline T$ of $T$ (respectively, for $T$) entails that Weyl's theorem holds for $T$ (respectively, for $\overline T$).

Sato's universal Grassmannian and group extensions

1991

An extension \(\widehat{GL}\) of the symmetry group GL of Sato's universal Grassmannian GM is constructed. The extension plays a similar role to that of the central extension \(\widehat{GL}_{{\text{res}}}\) in the approach of Segal and Wilson to τ functions and KP hierarchy. Our group G contains GLres as a subgroup and the associated τ function is a deformation of the usual τ function, leading to a deformed KP hierarchy. A relation to current algebra of Yang-Mills theory in 3+1 dimension is discussed.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

2009

Remark on integrable Hamiltonian systems

1980

An extension ton degrees of freedom of the fact is established that forn=1 the time and the energy constant are canonically conjugate variables. This extension is useful in some cases to get action-angle variables from the general solution of a given integrable Hamiltonian system. As an example the Delaunay variables are proved to be canonical.

Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

2019

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…

Sobolev homeomorphic extensions onto John domains

2020

Abstract Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the classical Jordan-Schoenflies theorem may admit no solution - it is possible to have a boundary homeomorphism which admits a continuous W 1 , 2 -extension but not even a homeomorphic W 1 , 1 -extension. We prove that if the target is assumed to be a John disk, then any boundary homeomorphism from the unit circle admits a Sobolev homeomorphic extension for all exponents p 2 . John disks, being one sided quasidisks, are of fundamental importance in Geometric Function The…

Weighted estimates for diffeomorphic extensions of homeomorphisms

2019

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the relationship between weighted integrability of the derivatives of $h$ and double integrals of $\varphi$ and of $\varphi^{-1} .$