Related papers: On the Translation Invariance of Wavelet Subspaces

We present an application of error theory using Dirichlet Forms in linear partial differential equations (LPDE). We study the transmission of an uncertainty on the terminal condition to the solution of the LPDE thanks to the decomposition…

In continuation of Part I, we study translative integral formulas for certain translation invariant functionals, which are defined on general convex bodies. Again, we consider local extensions and use these to show that the translative…

We prove a result of equivalence invariance of formal category theory for statements that can be expressed within an equipment. To do this, we exploit Henry and Bardomiano Mart\'inez's link between Makkai's FOLDS (first order logic with…

It is proven that if an interpolation map between two wavelet sets preserves the union of the sets, then the pair must be an interpolation pair. We also construct an example of a pair of wavelet sets for which the congruence domains of the…

We construct a wavelet and a generalised Fourier basis with respect to some fractal measures given by one-dimensional iterated function systems. In this paper we will not assume that these systems are given by linear contractions…

Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…

Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…

We extend the scope of noncommutative geometry by generalizing the construction of the noncommutative algebra of a quotient space to situations in which one is no longer dealing with an equivalence relation. For these so-called tolerance…

Partial transpose is an important operation for quantifying the entanglement, here we study the (partial) transpose of any single (two-mode) operators. Using the Fock-basis expansion, it is found that the transposed operator of an arbitrary…

A Hilbert module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We use the bracket product to construct some Hilbert modules over a group C*-algebra which…

In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. This provides a mathematical explanation for the emergence of…

In this paper we present a criteria to obtain interpolations formulas in terms of the sequence $\left(\{T_n(f)(Nm)\}\}_{m\in\mathbb{Z}}\right)_{n=1}^N$, where $f$ are functions whose Fourier transform is supported in $[-1/2,1/2]$, and $T_n$…

We introduce a fast Fourier transform on regular d-dimensional lattices. We investigate properties of congruence class representants, i.e. their ordering, to classify directions and derive a Cooley-Tukey-Algorithm. Despite the fast Fourier…

Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

This paper is devoted to the study of operator-valued Hardy spaces via wavelet method. This approach is parallel to that in noncommutative martingale case. We show that our Hardy spaces defined by wavelet coincide with those introduced by…

Assume that a linear space of real polynomials in $d$ variables is given which is translation and dilation invariant. We show that if a sequence in this space converges pointwise to a polynomial, then the limit polynomial belongs to the…

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the…

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the…