Search results for " Operator"

Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property

AbstractLet X be a Banach space. For describing the space P(C[0,1],X) of absolutely summing operators from C[0,1] to X in terms of the space X itself, we construct a tree space ℓ1tree(X) on X. It consists of special trees in X which we call two-trunk trees. We prove that P(C[0,1],X) is isometrically isomorphic to ℓ1tree(X). As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X∗-valued sequence spaces.

On the Bishop-Phelps-Bollobás type theorems

2017

This dissertation is devoted to the study of the Bishop-Phelps-Bollobás property in different contexts. In Chapter 1 we give a historical resume and the motivation behind this property as the classics Bishop-Phelps and Bishop-Phelps-Bollobás theorems. We define the Bishop-Phelps-Bollobás property (BPBp) and we comment on some important current results. In Chapter 2 we study similar properties to the BPBp. First, we define the Bishop-Phelps-Bollobás point property (BPBpp). The BPBpp is stronger than the BPBp. We study it for bounded linear operators and then for bilinear mappings. After that, we study two more similar properties: properties 1 and 2. Property 2 is just the dual property of th…

Essential norm estimates for composition operators on BMOA

2013

Abstract We provide two function-theoretic estimates for the essential norm of a composition operator C φ acting on the space BMOA; one in terms of the n-th power φ n of the symbol φ and one which involves the Nevanlinna counting function. We also show that if the symbol φ is univalent, then the essential norm of C φ is comparable to its essential norm on the Bloch space.

Fundamental solutions for general anisotropic multi-field materials based on spherical harmonics expansions

2016

Abstract A unified method to evaluate the fundamental solutions for generally anisotropic multi-field materials is presented. Based on the relation between the Rayleigh expansion and the three-dimensional Fourier representation of a homogenous partial differential operator, the proposed technique allows to obtain the fundamental solutions and their derivatives up to the desired order as convergent series of spherical harmonics. For a given material, the coefficients of the series are computed only once, and the derivatives of the fundamental solutions are obtained without any term-by-term differentiation, making the proposed approach attractive for boundary integral formulations and efficie…

PDE triangular Bézier surfaces: Harmonic, biharmonic and isotropic surfaces

2011

We approach surface design by solving second-order and fourth-order Partial Differential Equations (PDEs). We present many methods for designing triangular Bézier PDE surfaces given different sets of prescribed control points and including the special cases of harmonic and biharmonic surfaces. Moreover, we introduce and study a second-order and a fourth-order symmetric operator to overcome the anisotropy drawback of the harmonic and biharmonic operators over triangular Bézier surfaces. © 2010 Elsevier B.V. All rights reserved.

Exponential instability in the fractional Calder\'on problem

2017

In this note we prove the exponential instability of the fractional Calder\'on problem and thus prove the optimality of the logarithmic stability estimate from \cite{RS17}. In order to infer this result, we follow the strategy introduced by Mandache in \cite{M01} for the standard Calder\'on problem. Here we exploit a close relation between the fractional Calder\'on problem and the classical Poisson operator. Moreover, using the construction of a suitable orthonormal basis, we also prove (almost) optimality of the Runge approximation result for the fractional Laplacian, which was derived in \cite{RS17}. Finally, in one dimension, we show a close relation between the fractional Calder\'on pro…

A model of capillary phenomena in RN with subcritical growth

2020

This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p-Laplacian-like di¤erential operator in RN. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.

THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS

2018

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.

INTEGRAL SOLUTIONS TO A CLASS OF NONLOCAL EVOLUTION EQUATIONS

2010

We study the existence of integral solutions to a class of nonlinear evolution equations of the form [Formula: see text] where A : D(A) ⊆ X → 2X is an m-accretive operator on a Banach space X, and f : [0, T] × X → X and [Formula: see text] are given functions. We obtain sufficient conditions for this problem to have a unique integral solution.

Existence results and asymptotic behavior for nonlocal abstract Cauchy problems

2008

AbstractThe purpose of this paper is to study the existence and asymptotic behavior of solutions for Cauchy problems with nonlocal initial datum generated by accretive operators in Banach spaces.