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Local means and wavelets in function spaces

Hans Triebel (2008)

Banach Center Publications

The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type B p q s and F p q s on ℝⁿ and on ⁿ.

Local properties of accessible injective operator ideals

F. Oertel (1998)

Czechoslovak Mathematical Journal

In addition to Pisier’s counterexample of a non-accessible maximal Banach ideal, we will give a large class of maximal Banach ideals which are accessible. The first step is implied by the observation that a “good behaviour” of trace duality, which is canonically induced by conjugate operator ideals can be extended to adjoint Banach ideals, if and only if these adjoint ideals satisfy an accessibility condition (theorem 3.1). This observation leads in a natural way to a characterization of accessible...

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions g P g , ϕ , where for a fixed function ϕ, P g , ϕ denotes the one-dimensional orthogonal projection on the function U g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open, relatively...

Local/global uniform approximation of real-valued continuous functions

Anthony W. Hager (2011)

Commentationes Mathematicae Universitatis Carolinae

For a Tychonoff space X , C ( X ) is the lattice-ordered group ( l -group) of real-valued continuous functions on X , and C * ( X ) is the sub- l -group of bounded functions. A property that X might have is (AP) whenever G is a divisible sub- l -group of C * ( X ) , containing the constant function 1, and separating points from closed sets in X , then any function in C ( X ) can be approximated uniformly over X by functions which are locally in G . The vector lattice version of the Stone-Weierstrass Theorem is more-or-less equivalent...

Localization of bounded sets in tensor products.

A. Peris, M. J. Rivera (1996)

Revista Matemática de la Universidad Complutense de Madrid

The problem of topologies of Grothendieck is considered for complete tensor products of Fréchet spaces endowed with the topology defined by an arbitrary tensor norm. Some consequences on the stability of certain locally convex properties in spaces of operators are also given.

Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set Ω n . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization P m , Θ of the principal part P m is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for P m , Θ . Under additional assumptions P m must be locally hyperbolic.

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