Related papers: On the Translation Invariance of Wavelet Subspaces
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
We introduce and study the notions of translation bounded tempered distributions, and autocorrelation for a tempered distrubution. We further introduce the spaces of weakly, strongly and null weakly almost periodic tempered distributions…
We apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…
This paper is a study of first-order coherent logic from the point of view of duality and categorical logic. We prove a duality theorem between coherent hyperdoctrines and open polyadic Priestley spaces, which we subsequently apply to prove…
Associated with a given suitable function, or a measure, on $\mathbb{R}$, we introduce a correlation function, so that the Wronskian of the Fourier transform of the function is the Fourier transform of the corresponding correlation…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
The explicit integrability of second order ordinary differential equations invariant under time-translation and rescaling is investigated. Quadratic systems generated from the linearisable version of this class of equations are analysed to…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that…
We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…
A full interpolation theory for Sobolev functions with smoothness between 0 and 1 and vanishing trace on a part of the boundary of an open set is established. Geometric assumptions are of mostly measure theoretic nature and reach beyond…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.
Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical…
Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is…
We prove and construct Shannon-like Parseval wavelet frames for a class of two step connected, and simply connected nilpotent Lie groups, using a mixture of representation theory, group Fourier theory, and Gabor theory. Moreover, we are…
The Rademacher series in rearrangement invariant function spaces "closed" to the space L_\infty are considered. In terms of interpolation theory of operators a correspondence between such spaces and spaces of coefficients generated by them…
The lower invariance under a given arbitrary group of diffeomorphisms extends the notion of quasiconvexity. The non-commutativity of the group operation (the function composition) modifies the classical equivalence between lower…
We consider a class of convergence questions for infinite products that arise in wavelet theory when the wavelet filters are more singular than is traditionally built into the assumptions. We establish pointwise convergence properties for…