Search results for "Functional analysis"
showing 10 items of 1059 documents
The approximate subdifferential of composite functions
1993
This paper deals with the approximate subdifferential chain rule in a Banach space. It establishes specific results when the real-valued function is locally Lipschitzian and the mapping is strongly compactly Lipschitzian.
Dynamics, Operator Theory, and Infinite Holomorphy
2014
The works on linear dynamics in the last two decades show that many, even quite natural, linear dynamical systems exhibit wild behaviour. Linear chaos and hypercyclicity have been at the crossroads of several areas of mathematics. More recently, fascinating new connections have started to be explored: operators on spaces of analytic functions, semigroups and applications to partial differential equations, complex dynamics, and ergodic theory. Related aspects of functional analysis are the study of linear operators on Banach spaces by using geometric, topological, and algebraic techniques, the works on the geometry of Banach spaces and Banach algebras, and the study of the geometry of a Bana…
In between the inequalities of Sobolev and Hardy
2016
We establish both sufficient and necessary conditions for the validity of the so-called Hardy–Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev inequalities and the (weighted) Hardy inequalities. The Assouad dimension of the complement of the open set turns out to play an important role in both sufficient and necessary conditions. peerReviewed
Sharp generalized Trudinger inequalities via truncation
2006
Abstract We prove that the generalized Trudinger inequalities into exponential and double exponential Orlicz spaces improve to inequalities on Orlicz–Lorentz spaces provided they are stable under truncation.
Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
1994
In this paper we introduce qualification conditions for multivalued functions in Banach spaces involving the A-approximate subdifferential, and we show that these conditions guarantee metric regularity of multivalued functions. The results are then applied for deriving Lagrange multipliers of Fritz—John type and Kuhn—Tucker type for infinite non-smooth vector optimization problems.
Muckenhoupt $A_p$-properties of distance functions and applications to Hardy-Sobolev -type inequalities
2017
Let $X$ be a metric space equipped with a doubling measure. We consider weights $w(x)=\operatorname{dist}(x,E)^{-\alpha}$, where $E$ is a closed set in $X$ and $\alpha\in\mathbb R$. We establish sharp conditions, based on the Assouad (co)dimension of $E$, for the inclusion of $w$ in Muckenhoupt's $A_p$ classes of weights, $1\le p<\infty$. With the help of general $A_p$-weighted embedding results, we then prove (global) Hardy-Sobolev inequalities and also fractional versions of such inequalities in the setting of metric spaces.
Weyl symbols and boundedness of Toeplitz operators
2019
International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.
Noncommutative Davis type decompositions and applications
2018
We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz functions that…
Regularity of some method of summation for double sequences
2010
Some generalization of Toeplitz method of summation is introduced for double sequences and condition of regularity of it is obtained.
Unbounded C*-seminorms, biweights and *-representations of partial *-algebras: a review
2006
The notion of (unbounded) C*-seminorms plays a relevant role in the representation theory of *-algebras and partial *-algebras. A rather complete analysis of the case of *-algebras has given rise to a series of interesting concepts like that of semifinite C*-seminorm and spectral C*-seminorm that give information on the properties of *-representations of the given *-algebra A and also on the structure of the *-algebra itself, in particular when A is endowed with a locally convex topology. Some of these results extend to partial *-algebras too. The state of the art on this topic is reviewed in this paper, where the possibility of constructing unbounded C*-seminorms from certain families of p…