Related papers: Multiresolution Analysis for Compactly Supported I…

In this paper we use the equivalence result originally proved by the author which relates a multi-resolution analysis (MRA) of $L^2(R)$ and an orthonormal set of single electron wave-functions in the lowest Landau level, to build up a…

In this paper, we investigate whether the tensor product of two frames, each individually localised with respect to a spectral matrix algebra, is also localised with respect to a suitably chosen tensor product algebra. We provide a partial…

In statistical learning theory, interpolation spaces of the form $[\mathrm{L}^2,H]_{\theta,r}$, where $H$ is a reproducing kernel Hilbert space, are in widespread use. So far, however, they are only well understood for fine index $r=2$. We…

Motivated by recent applications of weighted norm inequalities to maximal regularity of first and second order Cauchy problems, we study real interpolation spaces on the basis of general Banach function spaces and, in particular, weighted…

In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these…

We consider integrable category $\mathcal{O}$ representations of Borcherds--Kac--Moody algebras whose Cartan matrix is finite dimensional, and determine the necessary and sufficient conditions for which the tensor product of irreducible…

Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…

Rapidly decaying kernels and frames (needlets) in the context of tensor product Jacobi polynomials are developed based on several constructions of multivariate $C^\infty$ cutoff functions. These tools are further employed to the development…

We study Banach spaces $C(K)$ of real-valued continuous functions from the finite product of compact lines. It turns out that the topological character of these compact lines can be used to distinguish whether two spaces of continuous…

We analyze the decomposition of tensor products between infinite dimensional (unitary) and finite-dimensional (non-unitary) representations of SL(2,R). Using classical results on indefinite inner product spaces, we derive explicit…

In the multicentric calculus one takes a polynomial with simple roots as a new global variable and replaces scalar functions {\varphi} by functions f taking values in C^d with d the degree of the polynomial leading to an efficient…

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…

We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This approach allows for the construction of generalized…

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…

We study real interpolation, but instead of interpolating between Banach spaces, we interpolate between general functions taking values in $[0,\infty].$ We show the equivalence of the mean method and the $K$-method and apply the general…

We determine the submodule of finite support of the tensor product of two modules M and N over a local ring and estimate its length in terms of $M$ and $N$. Also, we compute higher local cohomology modules of tensor products in a serial of…

This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for…

We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh,…

The tensor product of props was defined by Hackney and Robertson as an extension of the Boardman-Vogt product of operads to more general monoidal theories. Theories that factor as tensor products include the theory of commutative monoids…

Using the tensor identity, we obtain decomposition results for the tensor product of a generalized Verma module with a module $M$ in the category $\mathcal{O}^{\mathfrak{p}}$, based on the decomposition of the restriction of $M$ to the…