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Pointwise smoothness, two-microlocalization and wavelet coefficients.

Stéphane Jaffard (1991)

Publicacions Matemàtiques

In this paper we shall compare three notions of pointwise smoothness: the usual definition, J.M. Bony's two-microlocal spaces Cx0s,s', and the corresponding definition on the wavelet coefficients. The purpose is mainly to show that these two-microlocal spaces provide "good substitutes" for the pointwise Hölder regularity condition; they can be very precisely compared with this condition, they have more functional properties, and can be characterized by conditions on the wavelet coefficients. We...

Poisson's equation and characterizations of reflexivity of Banach spaces

Vladimir P. Fonf, Michael Lin, Przemysław Wojtaszczyk (2011)

Colloquium Mathematicae

Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality x ∈ X : s u p n | | ∑ k = 1 n T k x | | < ∞ = (I-T)X . We then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup T t : t ≥ 0 with generator A satisfies A X = x ∈ X : s u p s > 0 | | ∫ 0 s T t x d t | | < ∞ . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for the ranges...

Polar lattices from the point of view of nuclear spaces.

Wojciech Banaszczyk (1989)

Revista Matemática de la Universidad Complutense de Madrid

The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.

Polynomial functions on the classical projective spaces

Yu. I. Lyubich, O. A. Shatalova (2005)

Studia Mathematica

The polynomial functions on a projective space over a field = ℝ, ℂ or ℍ come from the corresponding sphere via the Hopf fibration. The main theorem states that every polynomial function ϕ(x) of degree d is a linear combination of “elementary” functions | ⟨ x , · ⟩ | d .

Polynomial inequalities in Banach spaces

Mirosław Baran (2015)

Banach Center Publications

We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.

Positive bases in ordered subspaces with the Riesz decomposition property

Vasilios Katsikis, Ioannis A. Polyrakis (2006)

Studia Mathematica

In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family ℱ = f i | i ∈ ℕ of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | f i ( x ) ≥ 0 for each i, and we study the existence of positive (Schauder) bases in ordered subspaces X of E with the Riesz decomposition property. We consider the elements x of E as sequences x = ( f i ( x ) ) and we develop a process of successive decompositions of a quasi-interior point of X₊ which at each step gives elements with smaller support....

Preduals of Sobolev-Campanato spaces

Konrad Gröger, Lutz Recke (2001)

Mathematica Bohemica

We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.

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