Related papers: A Class of Orthogonal Sequences

One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these…

Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…

We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical…

In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and…

We consider a Fermat curve $F_n:x^n+y^n+z^n=1$ over an algebraically closed field $k$ of characteristic $p\geq0$ and study the action of the automorphism group $G=\left(\mathbb{Z}/n\mathbb{Z}\times\mathbb{Z}/n\mathbb{Z}\right)\rtimes S_3$…

An orthoset (also called an orthogonality space) is a set $X$ equipped with a symmetric and irreflexive binary relation $\perp$, called the orthogonality relation. In quantum physics, orthosets play a central role. In fact, a Hilbert space…

This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor…

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…

We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…

In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…

We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.

We explore a class of meromorphic functions on elliptic curves, termed \emph{elliptic orthogonal a-polynomials} ($a$-EOPs), which extend the classical notion of orthogonal polynomials to compact Riemann surfaces of genus one. Building on…

We present a form convergence theorem for sequences of sectorial forms and their associated semigroups in a complex Hilbert space. Roughly speaking, the approximating forms $a_n$ are all `bounded below' by the limiting form $a$, but in…

This paper describes a class of sequences that are in many ways similar to Fibonacci sequences: given n, sum the previous two terms and divide them by the largest possible power of n. The behavior of such sequences depends on n. We analyze…

Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In \cite{HLL2023Te,LH2023Se}, $p$-ary self-orthogonal codes were constructed by using $p$-ary weakly regular bent…

We consider finite graphs whose vertexes are supersingular elliptic curves, possibly with level structure, and edges are isogenies. They can be applied to the study of modular forms and to isogeny based cryptography. The main result of this…

This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…

In this work, we define an orthogonal graph on the set of equivalence classes of $(2\nu + \delta)-$tuples over $\mathbb{Z}_{2^n}$ where $n$ and $\nu$ are positive integers and $\delta = 0, 1$ or $2$. We classify our graph if it is strongly…

We present in this paper a new method to deal with automatic sequences. This method allows us to prove a M\"obius-randomness-principle for automatic sequences from which we deduce the Sarnak conjecture for this class of sequences.…