Related papers: Demystifying Carleson Frames

We study the real, bounded-variables process (X_n) defined by a k-term recurrence relation X_{n+k} ={\phi}(X_n, ... , X_{n+k-1}). We prove the decay of correlations, mainly under purely analytic hypotheses concerning the function {\phi} and…

Frame theory is an exciting, dynamic and fast paced subject with applications in numerous fields of mathematics and engineering. In this paper we study Continuous Frame and introduce Continuous Frame with $C^{\ast}$-valued bounds. Also, we…

For $k \geqslant 0$, we define a simple topological graph $G$ (that is, a graph drawn in the plane such that every pair of edges intersect at most once, including endpoints) to be $k$-matching-planar if for every edge $e \in E(G)$, every…

For a big tt-category, we give a characterization of the Telescope Conjecture (TC) in terms of definable tensor-ideals generated by homological residue fields. We formulate a stalk-locality property of (TC) and prove that it holds in the…

We prove that for fixed $k$, every $k$-uniform hypergraph on $n$ vertices and of minimum codegree at least $n/2+o(n)$ contains every spanning tight $k$-tree of bounded vertex degree as a sub\-graph. This generalises a well-known result of…

A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…

We study properties of random subcomplexes of partitions returned by (a suitable form of) the Strong Hypergraph Regularity Lemma, which we call regular slices. We argue that these subcomplexes capture many important structural properties of…

Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities,…

We show that the potential of the scalar field in the Einstein frame is flat if the nonminimal coupling term is properly chosen that it satisfies the condition (V(phi)/K^2(phi)-> constant) as phi gets large. The cosmological implication of…

A bound on consecutive clique numbers of graphs is established. This bound is evaluated and shown to often be much better than the bound of the Kruskal-Katona theorem. A bound on non-consecutive clique numbers is also proven.

Denote by $\mathbf C_k[\mathfrak M]$ the $C_k$-stable closure of the class $\mathfrak M$ of all metrizable spaces, i.e., $\mathbf C_k[\mathfrak M]$ is the smallest class of topological spaces that contains $\mathfrak M$ and is closed under…

In this paper, we extend original Neural Collapse Phenomenon by proving Generalized Neural Collapse hypothesis. We obtain Grassmannian Frame structure from the optimization and generalization of classification. This structure maximally…

We study the existence of finite characterisations for modal formulas. A finite characterisation of a modal formula $\varphi$ is a finite collection of positive and negative examples that distinguishes $\varphi$ from every other,…

Each acyclic graph, and more generally, each acyclic orientation of the graph associated to a Cartan matrix, allows to define a so-called frise; this is a collection of sequences over the positive natural numbers, one for each vertex of the…

Let k be any field. J-P. Serre proved that the spectrum of the Grothendieck ring of the k-representation category of a group is connected, and that the same holds in characteristic zero for the representation category of a Lie algebra over…

Let $\{f_n:n\in\mathbb{N}\}$ be a $J$-frame for a Krein space ${\textbf{\textit{K}}}$ and $P_M$ be a $J$-orthogonal projection from ${\textbf{\textit{K}}}$ onto a subspace $M$. In this article we find sufficient conditions under which…

We show that for any constant $\mu>0$ and $k\ge 3$, there exists $\alpha>0$ such that the following holds for sufficiently large $n \in \mathbb{N}$. If $G=(V_{1},\ldots,V_{k},E)$ is a spanning subgraph of the $n$-blow-up of $K_{k}$ with…

We develop a family of simple rank one theories built over quite arbitrary sequences of finite hypergraphs. (This extends an idea from the recent proof that Keisler's order has continuum many classes, however, the construction does not…

We study Non-autonomous Iterated Function Systems (NIFSs) with overlaps. A NIFS on a compact subset $X\subset\mathbb{R}^m$ is a sequence $\Phi=(\{\phi^{(j)}_{i}\}_{i\in I^{(j)}})_{j=1}^{\infty}$ of collections of uniformly contracting maps…

We strengthen the Carleson-Hunt theorem by proving $L^p$ estimates for the $r$-variation of the partial sum operators for Fourier series and integrals, for $p>\max\{r',2\}$. Four appendices are concerned with transference, a variation norm…