相关论文: Wavelet sets without groups

We investigate the invariance properties of general wavelet coorbit spaces and Besov-type decomposition spaces under dilations by matrices. We show that these matrices can be characterized by quasi-isometry properties with respect to a…

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…

A wavelet-like model for distributions of objects in natural and man-made terrestrial environments is developed. The model is constructed in a self-similar fashion, with the sizes, amplitudes, and numbers of objects occurring at a constant…

Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for…

We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have…

Fix $A$, a family of subsets of natural numbers, and let $G_A(n)$ be the maximum cardinality of a subset of $\{1,2,..., n\}$ that does not have any subset in $A$. We consider the general problem of giving upper bounds on $G_A(n)$ and give…

Gabardo and Nashed have studied nonuniform wavelets based on the theory of spectral pairs for which the associated translation set $\Lambda =\left\{ 0,r/N\right\}+2\,\mathbb Z$ is no longer a discrete subgroup of $\mathbb R$ but a spectrum…

We report a special phenomenon: trailing waves. They are generated by the propagation of elastic waves in plates at large frequency-thickness (fd) product. Unlike lamb waves and bulk waves, trailing waves are a list of non-dispersive pulses…

Let $G$ be a finite abelian group and $A$ be a subset of $G$. We say that $A$ is complete if every element of $G$ can be represented as a sum of different elements of $A$. In this paper, we study the following question: {\it What is the…

We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…

Let $G$ be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on $G$ via the multiresolution analysis method. In this article, a characterization of wavelet sets on $G$ is established, which provides another method for the…

This paper develops methods based on coarse geometry for the comparison of wavelet coorbit spaces defined by different dilation groups, with emphasis on establishing a unified approach to both irreducible and reducible quasi-regular…

In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…

A set $B$ is a basis for a vector space $V$ if every element of $V$ can be uniquely written as a linear combination of the elements of $B$. There is a similar definition of a basis for a finite group. We show that certain semidirect…

We consider the 2-generated free metabelian associative and Lie algebras over the complex field and the invariants of the dihedral groups of finite order acting on these algebras. In the associative case we find a finite set of generators…

A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…

We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a…

Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we…

It is an open problem whether any pair of Bessel sequences with wavelet structure can be extended to a pair of dual frames by adding a pair of singly generated wavelet systems. We consider the particular case where the given wavelet systems…

In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…