## THE SPECTRUM OF VOLTERRA OPERATORS ON WEIGHTED SPACES OF ENTIRE FUNCTIONS

in** The Quarterly Journal of Mathematics**

September 2015; p ublished online June 2015 .

Journal Article. Subjects: Pure Mathematics. 4544 words.

We investigate the spectrum of the Volterra operator [math] with symbol an entire function [math], when it acts on weighted Banach spaces [math] of entire functions with sup-norms and when...

## Numerical‐Radius‐Attaining Polynomials

in** The Quarterly Journal of Mathematics**

March 2003; p ublished online March 2003 .

Journal Article. Subjects: Pure Mathematics. 0 words.

In this paper we discuss a version of James theorem making use of polynomials which attain their numerical radius. In addition, we obtain a characterization of finite‐dimensional Banach...

Go to
** » ** abstract

##
On the dentability of weak*-*H*_{δ}
sets

_{δ}

in** The Quarterly Journal of Mathematics**

September 2005; p ublished online September 2005 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We state several conditions equivalent to weak^{*}-dentability for certain subsets of a dual Banach space which include both the compact case and a result of Ghoussoub and Maurey.

Go to
** » ** abstract

## The vector-valued nonhomogeneous Tb Theorem

in** International Mathematics Research Notices**

January 2014; p ublished online October 2012 .

Journal Article. Subjects: Mathematics. 12407 words.

This paper gives a Banach space-valued extension of the Tb theorem of Nazarov et al. [20] concerning the boundedness of singular integral operators with respect to a measure *μ*, which only...

Go to
** » ** abstract

## DUALITY IN SPACES OF LORCH ANALYTIC MAPPINGS

in** The Quarterly Journal of Mathematics**

September 2016; p ublished online September 2016 .

Journal Article. Subjects: Pure Mathematics. 4433 words.

For a complex Banach algebra [math], we study the strong dual of the Fréchet space [math] of the mappings [math] that are analytic in the sense of Lorch. First, we will show that [math] is...

## POLYNOMIAL NUMERICAL INDEX FOR SOME COMPLEX VECTOR-VALUED FUNCTION SPACES

in** The Quarterly Journal of Mathematics**

December 2008; p ublished online January 2008 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We study the relation between the polynomial numerical indices of a complex vector-valued function space and the ones of its range space. It is proved that the spaces *C*(*K*, *X*) and *L*null...

Go to
** » ** abstract

## SEMISIMPLE BANACH ALGEBRAS GENERATED BY STRONGLY CONTINUOUS REPRESENTATIONS OF MOORE GROUPS

in** The Quarterly Journal of Mathematics**

June 2008; p ublished online December 2007 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We prove that if τ is a strongly continuous bounded representation of a Moore group *G* on a Banach space *X*, and if the Arveson spectrum of τ is scattered, then the closure with respect to...

Go to
** » ** abstract

##
A NOTE ON FRAGMENTABILITY AND WEAK-*G*
_{
δ
} SETS

in** The Quarterly Journal of Mathematics**

June 2012; p ublished online June 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

In terms of fragmentability, we describe a new class of Banach spaces which may be *c*
_{0}-saturated but do not contain weak-*G*
_{
δ
} open...

Go to
** » ** abstract

## Non-linear fractional integro-differential systems with non-local conditions

in** IMA Journal of Mathematical Control and Information**

June 2016; p ublished online November 2014 .

Journal Article. Subjects: Mathematics. 4251 words.

We prove the existence of mild solutions of fractional integro-differential equations with non-local conditions in Banach spaces. Sufficient conditions for controllability of fractional...

## Operator splitting for abstract Cauchy problems

in** IMA Journal of Numerical Analysis**

July 1998; p ublished online July 1998 .

Journal Article. Subjects: Mathematics. 0 words.

The operator splitting technique is formulated for inhomogeneous abstract Cauchy problems in Banach spaces, and its convergence properties are analyzed using the concepts, familiar from...

Go to
** » ** abstract

## On a multistep method approximating a linear sectorial evolution equation

in** IMA Journal of Numerical Analysis**

July 2002; p ublished online July 2002 .

Journal Article. Subjects: Mathematics. 0 words.

This paper concerns the linear multistep approximation of an abstract dissipative linear sectorial evolution equation on a Banach space *X*. We study how well the semigroup generated by a...

Go to
** » ** abstract

##
*H*
^{∞} Functional Calculus and Maximal Inequalities for Semigroups of Contractions on Vector-Valued *L*
_{
p
}-Spaces

in** International Mathematics Research Notices**

January 2015; p ublished online July 2014 .

Journal Article. Subjects: Mathematics. 4509 words.

Let {*T*
_{
t
}}_{
t>0} be a strongly continuous semigroup of positive contractions on *L*
_{
p
}(*X*,*μ*) with...

Go to
** » ** abstract

## Optimal control for linear discrete-time systems with Markov perturbations in Hilbert spaces

in** IMA Journal of Mathematical Control and Information**

March 2009; p ublished online March 2009 .

Journal Article. Subjects: Mathematics. 0 words.

In this article, we discuss a quadratic control problem for linear discrete-time systems with Markov perturbations in Hilbert spaces, which is linked to a discrete-time Riccati equation...

Go to
** » ** abstract

## Oscillations in lossless propagation models: a Liapunov–Krasovskii approach

in** IMA Journal of Mathematical Control and Information**

March 2002; p ublished online March 2002 .

Journal Article. Subjects: Mathematics. 0 words.

This paper focuses on Forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability...

Go to
** » ** abstract

## UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

in** The Quarterly Journal of Mathematics**

December 2010; p ublished online April 2009 .

Journal Article. Subjects: Pure Mathematics. 0 words.

Homogeneous polynomials of degree 2 on the complex Banach space *c*
_{0}(ℓ_{
n
}
^{2}) are shown to have unique norm-preserving extension to the...

Go to
** » ** abstract

## COARSE AND UNIFORM EMBEDDINGS INTO REFLEXIVE SPACES

in** The Quarterly Journal of Mathematics**

September 2007; p ublished online June 2007 .

Journal Article. Subjects: Pure Mathematics. 0 words.

**Abstract**

Answering an old problem in nonlinear theory, we show that *c*
_{0} cannot be coarsely or uniformly embedded into a reflexive Banach space,...

Go to
** » ** abstract

##
PROJECTIVITY OF BANACH AND *C**-ALGEBRAS OF CONTINUOUS FIELDS

in** The Quarterly Journal of Mathematics**

June 2013; p ublished online March 2012 .

Journal Article. Subjects: Pure Mathematics. 0 words.

We give necessary and sufficient conditions for the left projectivity and biprojectivity of Banach algebras defined by locally trivial continuous fields of Banach algebras. We identify...

Go to
** » ** abstract

## Gâteaux differentiability of Lipschitz functions

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 4791 words.

This chapter presents the main results on Gâteaux differentiability of Lipschitz functions by recalling the notions of the Radon-Nikodým property (RNP) and null sets. The discussion focuses...

## The Oxford Handbook of Functional Data Analysis

November 2010; p ublished online August 2018 .

Book. Subjects: Science and Mathematics. 514 pages.

This handbook presents the state-of-the-art of the statistics dealing with functional data analysis. With contributions from international experts in the field, it discusses a wide range of...

Go to
** » ** abstract

##
Γ-Null and Γ*N*-Null Sets

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 10215 words.

This chapter introduces the notions of Γ-null and Γₙ-null sets, which are σ-ideals of subsets of a Banach space *X*. Γ-null set is key for the strongest known general Fréchet...