Related papers: Separation of zeros and a Hermite interpolation ba…
Primal-dual splitting involving proximity operators in order to be able to find some approximation to the minimizer for a general form of Tikhonov type functional is in the focus of this work. This approximation is produced by a pair of…
We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the Riemann zeta function whose spacing is 2.9125 times larger than the average spacing. This is deduced from the calculation of the…
This paper proves the approximate intermediate value theorem, constructively and from notably weak hypotheses: from pointwise rather than uniform continuity, without assuming that reals are presented with rational approximants, and without…
We study the maximum geometric independent set and clique problems in the streaming model. Given a collection of geometric objects arriving in an insertion only stream, the aim is to find a subset such that all objects in the subset are…
The ability to efficiently and accurately construct an inverse frame operator is critical for establishing the utility of numerical frame approximations. Recently, the admissible frame method was developed to approximate inverse frame…
Assuming the Riemann Hypothesis, it is known that there are infinitely many consecutive pairs of zeros of the Riemann zeta-function within 0.515396 times the average spacing. This is obtained using the method of Montgomery and Odlyzko. We…
We introduce and analyze BPALM and A-BPALM, two multi-block proximal alternating linearized minimization algorithms using Bregman distances for solving structured nonconvex problems. The objective function is the sum of a multi-block…
In recent years, non-Hermitian phases in classical and quantum systems have garnered significant attention. In particular, their intriguing band geometry offers a platform for exploring unique topological states and unconventional quantum…
In this paper, we propose and study several strongly convergent versions of the forward-reflected-backward splitting method of Malitsky and Tam for finding a zero of the sum of two monotone operators in a real Hilbert space. Our proposed…
We present a new closed form for the interpolating polynomial of the general univariate Hermite interpolation that requires only calculation of polynomial derivatives, instead of derivatives of rational functions. This result is used to…
The number of linear independent algebraic relations among elementary symmetric polynomial functions over finite fields is computed. An algorithm able to find all such relations is described. It is proved that the basis of the ideal of…
Many "real" inverse spectral data for periodic finite-gap operators (consisting of Riemann Surface with marked "infinite point", local parameter and divisors of poles) lead to operators with real but singular coefficients. These operators…
In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…
Retrieving a signal from its triple correlation spectrum, also called bispectrum, arises in a wide range of signal processing problems. Conventional methods do not provide an accurate inversion of bispectrum to the underlying signal. In…
Let $I\subseteq \Bbb N$ be a finite or infinite set and let ${(x_n)_{n\in I}}$ be a frame for a separable Hilbert space $\mathcal{H}$. Consider transmission of a signal $h\in\mathcal{H}$ where a finite subset $(\langle h,x_n\rangle)_{n\in…
Structured illumination can reject out-of-focus signal from a sample, enabling high-speed and high-contrast imaging over large areas with widefield detection optics. Currently, this optical-sectioning technique is limited by image…
Novel chirally symmetric fermion actions containing the minimum amount of fermion doubling have been recently proposed in the literature. We study the symmetries and renormalization of these actions and find that in each case, discrete…
The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient…
Let $z_{1},\ldots,z_{K}$ be distinct grid points. If $f_{k,0}$ is the prescribed value of a function at the grid point $z_{k}$, and $f_{k,r}$ the prescribed value of the $r$\foreignlanguage{american}{-th} derivative, for $1\leq r\leq…
We show that a sufficient density condition for Gabor systems with Hermite functions over lattices is not sufficient in general. This follows from a result on how zeros of the Zak transform determine the frame property of integer…