Search results for "Mathematica"
showing 10 items of 7971 documents
Fréchet Spaces of Holomorphic Functions without Copies of l 1
1996
Let X be a Banach space. Let Hw*(X*) the Frechet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.
On the Unit Ball of Operator-valued H 2-functions
2009
Let X be a complex Banach space and let H 2 (\( \mathbb{D} \), X) denote the space of X-valued analytic functions in the unit disc such that $$ \mathop {sup}\limits_{0 < r < 1} \int_0^{2\pi } {\left\| {F\left( {re^{it} } \right)} \right\|^2 \frac{{dt}} {{2\pi }} < \infty .} $$ It is shown that a function F belongs to the unit ball of H 2 ( \( \mathbb{D} \), X) if and only if there exist f∈H ∞ (\( \mathbb{D} \), X) and ϕ∈H ∞ (\( \mathbb{D} \)) such that $$ \left\| {f\left( z \right)} \right\|^2 + \left| {\varphi \left( z \right)} \right|^2 \leqslant 1 and F\left( z \right) = \frac{{f\left( z \right)}} {{1 - z\varphi \left( z \right)}} $$ for |z| < 1.
Commutators of linear and bilinear Hilbert transforms
2003
Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ( α 1 ) = sign ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…
Absolute continuity of mappings with finite geometric distortion
2015
Suppose that ⊂ R n is a domain with n ≥ 2. We show that a continuous, sense-preserving, open and discrete mapping of finite geometric outer distortion with KO(·,f) ∈ L 1/(n 1) loc () is absolutely continuous on almost every line parallel to the coordinate axes. Moreover, if U ⊂ is an open set with N(f,U) 0 depends only on n and on the maximum multiplicity N(f,U).
The Poincaré inequality is an open ended condition
2008
Let p > 1 and let (X,d,µ) be a complete metric measure space with µ Borel and doubling that admits a (1,p)-Poincare inequality. Then there exists e > 0 such that (X,d,µ) admits a (1,q)-Poincare inequality for every q > p - e, quantitatively.
BARGAINING WITH COMMITMENT UNDER AN UNCERTAIN DEADLINE
2006
We consider an infinite horizon bargaining game in which a deadline can arise with positive probability and where players possess an endogenous commitment device. We show that for any truncation of the game, the equilibrium agreement can only take place if the deadline arises within this finite horizon. Since the deadline is an uncertain event, the equilibrium exhibits agreements which are delayed with positive probability.
Znawca języka czy człowiek komunikujący się? O strukturze kompetencji językowo-komunikacyjnej ucznia klas IV–VI szkoły podstawowej wpisanej w podstaw…
2019
The article aims to answer two questions: how the language instruction framework was inscribed into the 2017/2018 Polish language curriculum and what image of the linguistic and communicative competence results from this document. The research method is based on the assumption that these two questions can be answered by analysing the cognitive operators used in the description of specific requirements. The article analyses the operators found in the ‘language instruction’ section of the curriculum. Within the linguistic and communicative competence, the document distinguishes among metalinguistic, analytical, linguistic (including normative and grammar-lexical competences) and communicative…
Commutator anomalies and the Fock bundle
1990
We show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic Fock spaces parametrized by vector potentials, and more generally, by splittings of the fermionic one-particle space into a pair of complementary subspaces. On the Lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies.
The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras
2018
The notion of the equationally-defined commutator was introduced and thoroughly investigated in (Czelakowski, 2015). In this work the properties of the equationally-defined commutator in quasivarieties generated by two-element algebras are examined. It is proved: If a quasivariety Q is generated by a finite set of two-element algebras, then the equationally-defined commutator of Q is additive (Theorem 3.1) Moreover it satisfies the associativity law (Theorem 3.6). The second result is strengthened if the quasivariety is generated by a single two-element algebra 2: If Q = SP(2), then the equationally-defined commutator of Q universally validates one of the following laws: [x,y] = x^y or [x,y…
Weak commutation relations of unbounded operators and applications
2011
Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.