Related papers: Representation theory and multilevel filters
A novel wavelet-like function is presented that makes it convenient to create filter banks given mainly two parameters that influence the focus area and the filter count. This is accomplished by computing the inverse Fourier transform of…
Let $X$ be a non-empty set and let $\mathcal{F}$ be any $C^{\ast}$-subalgebra of $\ell ^{\infty}(X)$ containing the constant functions. We show that the spectrum of $\mathcal{F}$ can be considered as a space of certain filters determined by…
This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by…
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…
We introduce a harmonic analysis for a class of affine iteration models in $\br^d$. Using Hilbert-space geometry, we develop a new duality notion for affine and contractive iterated function systems (IFSs) and we construct some identities…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures…
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way…
If $G$ is a Lie group, $H\subset G$ is a closed subgroup, and $\tau$ is a unitary representation of $H$, then the authors give a sufficient condition on $\xi\in i\mathfrak{g}^*$ to be in the wave front set of $\operatorname{Ind}_H^G\tau$.…
This is the first article in a two-part series containing some results on dimension estimates for $C^1$ iterated function systems and repellers. In this part, we prove that the upper box-counting dimension of the attractor of any $C^1$…
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…
We investigate Tree Iterated Function Systems (TIFSs), which we introduce in this paper. TIFSs are the generalizations of Iterated Function Systems in which we take the maps independently at each step and each block. In this paper, we give…
We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in $\O_n$ using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation…
We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective $C(\mathbb T^n)$-modules. Conversely, we show how cancellation properties for finitely generated projective modules over…
Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…
A unitary representation of a, possibly infinite dimensional, Lie group $G$ is called semibounded if the corresponding operators $i\dd\pi(x)$ from the derived representation are uniformly bounded from above on some non-empty open subset of…
Motivated by Bownik and Speegle's result on linear independence of wavelet Parseval frames, we consider affine systems (analogous to wavelet systems) defined on a second countable, locally compact abelian group $G$, where the translations…
Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…
We propose a filtering feature selection framework that considers subsets of features as paths in a graph, where a node is a feature and an edge indicates pairwise (customizable) relations among features, dealing with relevance and…