Search results for " space"

QUANTIZATION OPERATORS ON QUADRICS

2008

Beyond frames: Semi-frames and reproducing pairs

2017

Frames are nowadays a standard tool in many areas of mathematics, physics, and engineering. However, there are situations where it is difficult, even impossible, to design an appropriate frame. Thus there is room for generalizations, obtained by relaxing the constraints. A first case is that of semi-frames, in which one frame bound only is satisfied. Accordingly, one has to distinguish between upper and lower semi-frames. We will summarize this construction. Even more, one may get rid of both bounds, but then one needs two basic functions and one is led to the notion of reproducing pair. It turns out that every reproducing pair generates two Hilbert spaces, conjugate dual of each other. We …

A spectral mapping theorem for perturbed strongly continuous semigroups

1991

PIP-Spaces and Signal Processing

2009

Contemporary signal processing makes an extensive use of function spaces, always with the aim of getting a precise control on smoothness and decay properties of functions. In this chapter, we will discuss several classes of such function spaces that have found interesting applications, namely, mixed-norm spaces, amalgam spaces, modulation spaces, or Besov spaces. It turns out that all those spaces come in families indexed by one or more parameters, that specify, for instance, the local behavior or the asymptotic properties. In general, a single space, taken alone, does not have an intrinsic meaning, it is the family as a whole that does, which brings us to the very topic of this volume. In …

A note on quarkonial systems and multilevel partition of unity methods

2013

We discuss the connection between the theory of quarkonial decompositions for function spaces developed by Hans Triebel, and the multilevel partition of unity method. The central result is an alternative approach to the stability of quarkonial decompositions in Besov spaces , s > n(1/p − 1)+, which leads to relaxed decay assumptions on the elements of a quarkonial system as the monomial degree grows.

Properties of Generalized Polynomial Spaces in Three Variables

2009

Multivariate interpolation is a topic which often appears in practical modeling problems. Different type of spaces of functions are used for solving interpolation problems. When the interpolation conditions are of different kind, by example, spacial and temporal, one possibility for modeling the problem is to use a generalize degree, in which the monomials exponents are weighted with a weight vector with integer components. In order to use such a generalize polynomial space as interpolation space, it is necessary to know the dimension and a basis of it. The aim of this article is to study and prove many properties of the generalize polynomial spaces in three variables.

Ein Axiomensystem f�r partielle affine R�ume

1994

A partial linear space with parallelism is called partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. These partial affine spaces will be characterized by a system of three axioms for partial linear spaces with parallelism.

A probabilistic Weitzenböck formula on Riemannian path space

2000

Symmetric Surfaces with Many Singularities

2004

Abstract Let G ⊂ SO(4) denote a finite subgroup containing the Heisenberg group. In this paper we classify all such groups, we find the dimension of the spaces of G-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding G-invariant pencils of surfaces in ℙ3 which we started in Sarti [Sarti, A. (2000). Pencils of symmetric surfaces in ℙ3(C). J. Algebra 246:429–452]. It turns out that we have five more pencils, two of them containing surfaces with nodes.

Examples of improjective operators

2000

It has been an open question for some time whether improjective operators are always inessential. Here we give some examples that answer in the negative this question as well as some other related ones, posed in [2, 3, 11, 12]. The description of the examples uses a indecomposable space, constructed by Gowers and Maurey [5], and a characterization of the indecomposable Banach spaces in terms of improjective operators.