Search results for "predicate"
showing 10 items of 216 documents
Sobolev Extension on Lp-quasidisks
2021
AbstractIn this paper, we study the Sobolev extension property of Lp-quasidisks which are the generalizations of classical quasidisks. After that, we also find some applications of this property.
Local Spectral Theory
2018
In this chapter we shall introduce an important property, defined for bounded linear operators on complex Banach spaces, the so-called single-valued extension property (SVEP).
Some spectral mapping theorems through local spectral theory
2004
The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra. We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a re…
Traces of weighted function spaces: dyadic norms and Whitney extensions
2017
The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950's. In this paper we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well adapted to extending functions using the Whitney extension operator.
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients
2017
International audience; The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in space problem we establish energy estimates with finite loss of derivatives, which is linearly increasing in time. This implies well-posedness in H ∞ , if the coefficients enjoy enough smoothness in x. From this result, by standard arguments (i.e. extension and convexification) we deduce also local existence and uniqueness. A huge part of the analysis is devoted to give an appropriate sense to the Cauchy problem, which is not evide…
Cyclic (noncyclic) phi-condensing operator and its application to a system of differential equations
2019
We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.
Quasiextremal distance domains and extension of quasiconformal mappings
1985
On the stability of the localized single-valued extension property under commuting perturbations
2013
This article concerns the permanence of the single-valued extension property at a point under suitable perturbations. While this property is, in general, not preserved under sums and products of commuting operators, we obtain positive results in the case of commuting perturbations that are quasi-nilpotent, algebraic, or Riesz operators.