Related papers: Multiresolution Analysis for Compactly Supported I…
We show that there exist infinite-dimensional extremely non-complex Banach spaces, i.e. spaces $X$ such that the norm equality $\|Id + T^2\|=1 + \|T^2\|$ holds for every bounded linear operator $T:X\longrightarrow X$. This answers in the…
We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for…
We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold…
In this article we prove martingale type pointwise convergence theorems pertaining to tensor product splines defined on $d$-dimensional Euclidean space ($d$ is a positive integer), where conditional expectations are replaced by their…
We identify multiresolution subspaces giving rise via Hankel transforms to Bessel functions. They emerge as orthogonal systems derived from geometric Hilbert-space considerations, the same way the wavelet functions from a multiresolution…
The purpose of this paper is to present new classes of function systems as part of multiresolution analyses. Our approach is representation theoretic, and it makes use of generalized multiresolution function systems (MRSs). It further…
This semi-expository work covers central aspects of the theory of relative tensor products as developed in Higher Algebra, as well as their application to Koszul duality for algebras in monoidal oo-categories. Part of our goal is to expand…
We show the existence of smooth band-limited multiresolution analysis (MRA) for any expansive dilation with real entries in any spatial dimension. We then prove the existence of orthonormal Meyer wavelets, which have smooth and compactly…
Targeting at sparse learning, we construct Banach spaces B of functions on an input space X with the properties that (1) B possesses an l1 norm in the sense that it is isometrically isomorphic to the Banach space of integrable functions on…
The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…
In this paper, the $mn$-dimensional space of tensor-product polynomials of two variables, of degree at most $(m-1)+(n-1)$, is considered. A theory of two-variate polynomials is developed by establishing the algebra and basic algebraic…
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of…
In recent years finite tensor products of reproducing kernel Hilbert spaces (RKHSs) of Gaussian kernels on the one hand and of Hermite spaces on the other hand have been considered in tractability analysis of multivariate problems. In the…
Although tensor product real-valued wavelets have been successfully applied to many high-dimensional problems, they can only capture well edge singularities along the coordinate axis directions. As an alternative and improvement of tensor…
We consider tractability of integration in reproducing kernel Hilbert spaces which are a tensor product of a Walsh space and a Korobov space. The main result provides necessary and sufficient conditions for weak, polynomial and strong…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
Given any Banach space $X$ and any weak*-compact subset $K$ of $X^*$, we compute the Szlenk index of the weak*-closed, convex hull of $K$ as a function of the Szlenk index of $K$. Also as an application, we compute the Szlenk index of any…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
In earlier work a crossed product of a Banach algebra was constructed from a Banach algebra dynamical system $(A,G,\alpha)$ and a class $\mathcal{R}$ of continuous covariant representations, and its representations were determined. In this…
This is the first part of a series of two papers aiming to construct a categorification of the braiding on tensor products of Verma modules, and in particular of the Lawrence--Krammer--Bigelow representations. \\ In this part, we categorify…