Related papers: Super-wavelets on local fields of positive charact…
This paper presents a discussion on multiframelet set, multiwavelet set and set correspond to super wavelet on local fields of positive characteristic. We characterize Parseval multiframelet set and give equivalent conditions multiwavelet…
Using the wavelet theory introduced by the author and J. Benedetto, we present examples of wavelets on p-adic fields and other locally compact abelian groups with compact open subgroups. We observe that in this setting, the Haar and Shannon…
We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic…
We define an affine structure on $\ltwor\oplus...\oplus\ltwor$ and, following some ideas developed in \cite{Dut1}, we construct a local trace function for this situation. This trace function is a complete invariant for a shift invariant…
In this article we establish theory of semi-orthogonal Parseval wavelets associated to generalized multiresolution analysis (GMRA) for the local field of positive characteristics (LFPC). By employing the properties of translation invariant…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
This paper develops the use of wavelets as a basis set for the solution of physical problems exhibiting behavior over wide-ranges in length scale. In a simple diagrammatic language, this article reviews both the mathematical underpinnings…
Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G=Q_p, the field of p-adic rational numbers (as a group under addition), which has compact open subgroup H=Z_p, the ring of…
The classical characterization of \wp, as a typical concept for far field phenomena, has been successfully applied to many \w phenomena in past decades. The recent reports of superluminal tunnelling times and negative group velocities…
We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of…
We establish dilation theorems for non-tight frames with additional structure, i.e., frames generated by unitary groups of operators and projective unitary representations. This generalizes previous dilation results for Parseval frames due…
We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. In…
Motivated by potential applications in multiplexing and by recent results on Gabor analysis with Hermite windows due to Gr\"{o}chenig and Lyubarskii, we investigate vector-valued wavelet transforms and vector-valued wavelet frames, which…
We investigate the description of statistical field theories using Daubechies' orthonormal compact wavelets on a lattice. A simple variational approach is used to extend mean field theory and make predictions for the fluctuation strengths…
We first review the definition of superprojective spaces from the functor-of-points perspective. We derive the relation between superprojective spaces and supercosets in the framework of the theory of sheaves. As an application of the…
The local supertwistor formalism, which involves a superconformal connection acting on the bundle of such objects over superspace, is used to investigate superconformal geometry in six dimensions. The geometry corresponding to (1, 0) and…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
The classical Wilson loop is the gauge-invariant trace of the parallel transport around a closed path with respect to a connection on a vector bundle over a smooth manifold. We build a precise mathematical model of the super Wilson loop, an…
In this paper, we propose a new method for the construction of multi-dimensional, wavelet-like families of affine frames, commonly referred to as framelets, with specific directional characteristics, small and compact support in space,…
In the framework of wave packet analysis, finite wavelet systems are particular classes of finite wave packet systems. In this paper, using a scaling matrix on a permuted version of the discrete Fourier transform (DFT) of system generator,…