arXiv subjects

Rashid Aliev

Publications and source records attributed to Rashid Aliev.

5 recordsLinked to original sources

arXiv2026

Boundedness of the discrete Hilbert transform on discrete weighted Morrey spaces

The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in many areas of science and technology and plays an important role in digital signal processing. The essential motivation behind thinking about discrete transforms is that experimental data are most often not taken in a continuous manner but sampled at discrete time values. Since much of the data collected in both the physical sciences and engineering are discrete, the discrete Hilbert transform is a rather useful tool in these areas for the general analysis of this type of data. In this paper, we discuss the discrete Hilbert transform on discrete Weighted Morrey spaces and obtain its boundedness in these spaces.

math.FA↗

arXiv2025

On the Kurepa and inhomogeneous Cauchy functional equations

It follows from de Bruijn's results that if a continuous or $k$-th order continuously differentiable function $F(x,y)$ is a solution of the Kurepa functional equation, then it can be expressed as $F(x,y)=f(x+y)-f(x)-f(y)$ with the continuous $f$ or the $k$-th order continuously differentiable $f$, respectively. These two facts strengthen the corresponding results of Kurepa and Erdös. In this paper, we provide new and constructive proofs for these facts. In addition to practically useful recipes given here for construction of $f$, we also estimate its modulus of continuity.

math.CA↗

arXiv2020

The double difference property for the class of locally Hölder continuous functions

In this paper, we show that the pair of classes of locally Hölder continuous functions (considered on $\mathbb{R}$ and $\mathbb{R}^{2}$, respectively) has the double difference property.

math.CA↗

arXiv2020

A representation problem for smooth sums of ridge functions

In this paper we prove that if a multivariate function of a certain smoothness class is represented by a sum of $k$ arbitrarily behaved ridge functions, then it can be represented by a sum of $k$ ridge functions of the same smoothness class and a polynomial of degree at most $k-1$. This solves the problem posed by A. Pinkus in his monograph "Ridge Functions" up to a multivariate polynomial.

math.CA↗

arXiv2016

On the representation by bivariate ridge functions

We consider the problem of representation of a bivariate function by sums of ridge functions. We show that if a function of a certain smoothness class is represented by a sum of finitely many, arbitrarily behaved ridge functions, then it can also be represented by a sum of ridge functions of the same smoothness class. As an example, this result is applied to a homogeneous constant coefficient partial differential equation.

math.CA↗