Related papers: Cross-Gram Matrix associated to two sequences in H…

Let $\Gamma$ be a doubling graph satisfying some pointwise subgaussian estimates of the Markov kernel. We introduce a space $H^1(\Gamma)$ of functions and a space $H^1(T_\Gamma)$ of 1-forms and give various characterizations of them. We…

A sequence $\{g_k\}_{k=1}^\infty$ in a Hilbert space $\cal H$ has the expansion property if each $f\in \overline{\text{span}} \{g_k\}_{k=1}^\infty$ has a representation $f= \sum_{k=1}^\infty c_k g_k$ for some scalar coefficients $c_k.$ In…

To improve the numerical efficiency of iterative algorithms for inverting the frame operator, the controlled frame was introduced by Balazs et al. \cite{Balazs}, and has since been given more importance. In this paper, we introduce the…

If $R$ is a commutative ring, $M$ a compact $R$-oriented manifold and $G$ a finite graph without loops or multiple edges, we consider the graph configuration space $M^G$ and a Bendersky-Gitler type spectral sequence converging to the…

Let $\gamma = (\gamma_1,...,\gamma_N)$, $N \geq 2$, be a system of proper contractions on a complete metric space. Then there exists a unique self-similar non-empty compact subset $K$. We consider the union ${\mathcal G} = \cup_{i=1}^N…

The Graded Classification Conjecture (GCC) states that the pointed $K_0^{\operatorname{gr}}$-group is a complete invariant of the Leavitt path algebras of finite graphs when these algebras are considered with their natural grading by…

In this note, we fix a real invertible $d\times d$ matrix $\mathcal{A}$ and consider $\mathcal{A}\mathbb{Z}^d$ as an index set. For $f\in L^2(\mathbb{R}^d)$, let $\Phi^{\mathcal{A}}_{f}:=\frac{1}{|\det \mathcal{A}|}\sum_{k\in…

In a number of recent works [6, 7] the authors have introduced and studied a functor $\mathcal{F}_k$ which associates to each loose graph $\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a…

Frames in separable Hilbert spaces gives stable analysis and reconstruction of each vector in the underlying space. In this paper, we study frame conditions for a collection of matrix-valued functions obtained by non-uniform shifts. We give…

Let $H$ be a complex Hilbert space. Consider the ortho-Grassmann graph $\Gamma^{\perp}_{k}(H)$ whose vertices are $k$-dimensional subspaces of $H$ (projections of rank $k$) and two subspaces are connected by an edge in this graph if they…

This note concerns a further study about Riesz-Fischer maps, already introduced by the author in a recent work, that is a notion that extends to the spaces of distributions the sequences that are known as Riesz-Fischer sequences. In…

In a seminal paper, Kaminski, Kisielowski an Lewandowski for the first time extended the definition of spin foam models to arbitrary boundary graphs. This is a prerequisite in order to make contact to the canonical formulation of Loop…

We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, $\{f_i\}_{i \in \sigma} \cup \{g_i\}_{i \in…

It has been recently shown that if $K$ is a sesqui-analytic scalar valued non-negative definite kernel on a domain $\Omega$ in $\mathbb C^m$, then the function $\big(K^2\partial_i\bar{\partial}_j\log K\big )_{i,j=1}^ m,$ is also a…

A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hilbert space and creation operators which are partial isometries acting on the space. We call the…

Let (f_n) and (g_n) be two sequences of random variables adapted to an increasing sequence of $\sigma$-algebras $({\cal F}_n)$ such that the conditional distributions of f_n and g_n given ${\cal F}_{n-1}$ coincide, and such that the…

In previous papers we investigated basic properties of the determinant $G_{K}(s)$ of the Riemann operator: ${\mathcal R}$ acting on $\bigoplus_{n>1} K_{n}(A)_{\mathbb{C}}$, where $A$ is the integer ring of an algebraic number field $K$. The…