Related papers: Multiresolution Analysis for Compactly Supported I…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
We evaluate some methods designed for tensor- (or data-) based multivariate model construction (approximation and compression). To this aim, a collection of multivariate functions and an evaluation methodology are suggested. First, these…
Quasi *-algebras form an essential class of partial *-algebras, which are algebras of unbounded operators. In this work, we aim to construct tensor products of normed, respectively Banach quasi *-algebras, and study their capacity to…
When an approximant is accurate on the interval, it is only natural to try to extend it to several-dimensional domains. In the present article, we make use of the fact that linear rational barycentric interpolants converge rapidly toward…
Applications of the theory and computations of boolean matrices are of fundamental importance to study a variety of discrete structural models. But the increasing ability of data collection systems to store huge volumes of multidimensional…
Multiresolution analysis (MRA) on compact abelian group $G$ has been constructed with epimorphism as a dilation operator. We show a characterization of scaling sequences of an MRA on $L^p(G)$, $1\le p<\infty$. With the help of this scaling…
We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…
The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalised to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and…
This article begins the theory of submanifolds into products of 2 or more space forms. The tensors $\mathbf{R}$, $\mathbf{S}$ and $\mathbf{T}$ defined by Lira, Tojeiro and Vit\'orio at \cite{LTV} and the Bonnet theorem proved by them are…
The aim of this paper is to extend the notion of Apq space from its historical context in the work of Herz and to recognise such spaces as preduals of spaces of intertwining operators of induced representations as suggested by the work of…
It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an…
We study the classification of spaces of continuous functions $C(K)$ under positive linear maps. For infinite countable compacta, we show that whenever $C(K)$ and $C(L)$ are isomorphic, there exists an isomorphism $T:C(K)\to C(L)$…
We introduce a new construction of matrix wreath products of algebras that is similar to wreath products of groups. We then use it to prove embedding theorems for Jacobson radical, nil, and primitive algebras. In \S\ref{Section6}, we…
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…
An extension of Chernoff's product formula for one-parameter functions taking values in the space of bounded linear operators on a Banach space is given. Essentially, the $n$-th one-parameter function in the product formula is mapped by the…
Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…
We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…
Tensor products of ultrafilters have special combinatorial features closely related to Ramsey's Theorem, making them useful tools in applications. Here we first review their fundamental properties and isolate some new ones, including a…