Related papers: Demystifying Carleson Frames
We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in general graphs. These methods are of independent interest due…
In the light of $\phi$-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian $J(\phi/v)\neq0$. When…
We study the modal completeness and the finite frame property of several sublogics of the logic $\mathbf{IL}$ of interpretability with respect to Visser frames, which are also called simplified Veltman frames. Among other things, we prove…
We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…
This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized…
The Malmquist-Takenaka system is a perturbation of the classical trigonometric system, where powers of $z$ are replaced by products of other M\"obius transforms of the disc. The system is also inherently connected to the so-called nonlinear…
We prove that Jacobi, CMV, and Schr\"odinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely…
Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently…
Motivated by studies in accelerator physics this paper computes the asymptotic behavior of the series $\displaystyle \sum_{k=1}^N \varphi(k) I_N\left(\frac{1}{k}\right)$, where $\varphi(k)$ is Euler's Totient function and $\displaystyle…
Based on the shearlet transform we present a general construction of continuous tight frames for $L^2(\mathbb{R}^2)$ from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems,…
We develop a theory of $n \times n$-matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour $\Gamma$ is a finite union of simple closed Carleson curves in…
The Akbari-Cameron-Khosrovshahi (ACK) conjecture, which appears to be unresolved, states that for any simple graph $G$ with at least one edge, there exists a nonzero {$\{0,1\}$}-vector in the row space of its adjacency matrix that is not a…
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…
In 2016, a breakthrough result of Chechik and Wulff-Nilsen [SODA '16] established that every $n$-node graph $G$ has a $(1+\varepsilon)(2k-1)$-spanner of lightness $O_{\varepsilon}(n^{1/k})$, and recent followup work by Le and Solomon [STOC…
Our main result is that every graph $G$ on $n\ge 10^4r^3$ vertices with minimum degree $\delta(G) \ge (1 - 1 / 10^4 r^{3/2} ) n$ has a fractional $K_r$-decomposition. Combining this result with recent work of Barber, K\"uhn, Lo and Osthus…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We build on a recent result stating that the frame $\mathsf{SE}(L)$ of strongly exact filters for a frame $L$ is anti-isomorphic to the coframe $\mathsf{S}_o(L)$ of fitted sublocales. The collection $\mathsf{E}(L)$ of exact filters of $L$…
The results of Bergelson-Host-Kra and Leibman say that a multiple polynomial correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined by evaluating a continuous function along an orbit in a nilsystem) and a…