Related papers: Thin Sequences
The binomial interpolated transform of a sequence is a generalization of the well-known binomial transform. We examine a Pascal-like triangle, on which a binomial interpolated transform works between the left and right diagonals, focusing…
When we deal with $H^{\infty}$, it is known that $c_0-$interpolating sequences are interpolating and it is sufficient to interpolate idempotents of $\ell_\infty$ in order to interpolate the whole $\ell_\infty$. We will extend these results…
We denote by $\Hp$ the Hilbert space of ordinary Dirichlet series with square-summable coefficients. The main result is that a bounded sequence of points in the half-plane $\sigma >1/2$ is an interpolating sequence for $\Hp$ if and only if…
A sequence which is a finite union of interpolating sequences for $H^\infty$ have turned out to be especially important in the study of Bergman spaces. The Blaschke products $B(z)$ with such zero sequences have been shown to be exactly…
The goal of this article is to understand some interesting features of sequences of arbitrage operations, which look relevant to various processes in Economics and Finances. In the second part of the paper, analysis of sequences of…
In this paper we give an overview of recent results on (upper and lower) discrepancy estimates for (concrete) sequences in the unit-cube. In particular we also give an overview of discrepancy estimates for certain classes of hybrid…
We discuss supernear spaces.
We investigate algebraic structures within sets of surjective and injective linear operators between sequence spaces, completing results of Aron et al.
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
In the present paper we investigate distributional properties of sparse sequences modulo almost all prime numbers. We obtain new results for a wide class of sparse sequences which in particular find applications on additive problems and the…
This is a survey on discrete linear operators which, besides approximating in Jackson or near-best order, possess some interpolatory property at some nodes. Such operators can be useful in numerical analysis.
In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…
We propose two possible definitions for the notion of a sampling sequence (or set) for Hardy spaces of the disk. The first one is inspired by recent work of Bruna, Nicolau, and \O yma about interpolating sequences in the same spaces, and it…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.
The paper investigates the properties of a nonlinear recursive sequence which includes several ones studied formerly in the literature.