Related papers: Sieve functions in arithmetic bands, II

The aim of the paper is to study the limit distributions and the asymptotic behavior of summation arithmetic functions. A probabilistic approach based on the use of the axioms of probability theory is used for these purposes. Sufficient…

We prove that if $f:(a,b)\to\mathbb{R}$ is convex, then for any $\varepsilon>0$ there is a convex function $g\in C^2(a,b)$ such that $|\{f\neq g\}|<\varepsilon$ and $\Vert f-g\Vert_\infty<\varepsilon$.

In this paper we investigate continuity properties of functions $f:\mathbb{R}_+\to\mathbb{R}_+$ that satisfy the $(p,q)$-Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(f(x),f(y)) \qquad(x,y>0), $$ where $H_p$ stands for the…

Associativity of a two-place function $T: [0,1]^2\rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,\infty]^2\rightarrow[0,\infty]$ is an associative function, $f: [0,1]\rightarrow [0,\infty]$ is a monotone function…

An almost periodic function in finite-dimensional space extends to a holomorphic bounded function in a tube domain with a cone in the base if and only if the spectrum belongs to the conjugate cone. Also, an almost periodic function in…

We say that a function $\alpha(x)$ belongs to the set ${\bf A}^{(\gamma)}$ if it has an asymptotic expansion of the form $\alpha(x)\sim \sum^\infty_{i=0}\alpha_ix^{\gamma-i}$ as $x\to\infty$, which can be differentiated term by term…

In this document, prime numbers are related as functions over time, mimicking the Sieve of Eratosthenes. For this purpose, the mathematical representation is a uni-dimentional time line depicting the number line for positive natural numbers…

Let $T_{\epsilon}$, $0 \le \epsilon \le 1/2$, be the noise operator acting on functions on the boolean cube $\{0,1\}^n$. Let $f$ be a nonnegative function on $\{0,1\}^n$ and let $q \ge 1$. In arXiv:1809.09696 the $\ell_q$ norm of…

Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…

We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.

Let $f\colon\mathbb{N}\rightarrow\mathbb{C}$ be an arithmetic function and consider the Beatty set $\mathcal{B}(\alpha) = \lbrace\, \lfloor n\alpha \rfloor : n\in\mathbb{N} \,\rbrace$ associated to a real number $\alpha$, where…

Let $G=(G_j)_{j\ge 0}$ be a strictly increasing linear recurrent sequence of integers with $G_0=1$ having characteristic polynomial $X^{d}-a_1X^{d-1}-\cdots-a_{d-1}X-a_d$. It is well known that each positive integer $\nu$ can be uniquely…

Given integers s,t, define a function phi_{s,t} on the space of all formal series expansions by phi_{s,t} (sum a_n x^n) = sum a_{sn+t} x^n. For each function phi_{s,t}, we determine the collection of all rational functions whose Taylor…

In a recent work of the authors, we showed some general inequalities governing numerical radius inequalities using convex functions. In this article, we present results that complement the aforementioned inequalities. In particular, the new…

Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this…

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be…

For a geometrically finite group Gamma of G=SO(n,1), we survey recent developments on counting and equidistribution problems for orbits of Gamma in a homogeneous space H\G where H is trivial, symmetric or horospherical. Main applications…

Let $\{f_i:\mathbb{F}_p^i \to \{0,1\}\}$ be a sequence of functions, where $p$ is a fixed prime and $\mathbb{F}_p$ is the finite field of order $p$. The limit of the sequence can be syntactically defined using the notion of ultralimit.…

Let $g \geq 2$. A real number is said to be g-normal if its base g expansion contains every finite sequence of digits with the expected limiting frequency. Let \phi denote Euler's totient function, let \sigma be the sum-of-divisors…

Let $\ID$ denote the open unit disk and $f:\,\ID\TO\BAR\IC$ be meromorphic and univalent in $\ID$ with the simple pole at $p\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion…