Related papers: On the Bohr phenomenon for complex valued and vect…
We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.
This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform…
In this paper, we introduce and study the Weyl transform of functions which are integrable with respect to a vector measure on a phase space associated to a locally compact abelian group. We also study the Weyl transform of vector measures.…
In this paper, several Bohr-type inequalities are generalized to the form with two parameters for the bounded analytic function. Most of the results are sharp.
We study Caratheodory-Herglotz functions whose values are continuous operators from a locally convex topological space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case…
We define a scalar valued Fourier transform for functions on the Heisenberg group and establish some of its basic properties like inversion formula, Plancherel theorem and Riemann-Lebesgue lemma. We also restate certain well known theorems…
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension $d \leq 3$, vanishing Chern classes of bundles of Bloch eigenfunctions characterize operators with exponentially…
Let $T$ be a multilinear operator which is bounded on certain products of unweighted Lebesgue spaces of $\mathbb R^n$. We assume that the associated kernel of $T$ satisfies some mild regularity condition which is weaker than the usual…
In this paper, we have defined bicomplex valued functions of bounded variations and rectifiable hyperbolic path. We have studied the integration of product-type bicomplex functions over rectifiable hyperbolic path. Also we have established…
A crucial extension of quaternionic function theory to octonions is the concept of slice regular functions, introduced to handle holomorphic-like properties in a non-associative setting. In this paper, first we present a generalization of…
In this paper, we investigate the Bohr phenomenon for the class of analytic functions defined on the simply connected domain \begin{equation*} \Omega_{\gamma}=\bigg\{z\in\mathbb{C} :…
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is…
We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier…
We argue that there should exist a "noncommutative Fourier transform" which should identify functions of noncommutative variables (say, of matrices of indeterminate size) and ordinary functions or measures on the space of paths. Some…
The Bohr theorem states that any function $f(z) = \sum_{n=0}^{\infty} a_{n} z^{n}$, analytic and bounded in the open unit disk, obeys the inequality $\sum_{n=0}^{\infty} |a_{n}| |z|^{n} < 1$ in the open disk of radius 1/3, the so-called…
It is shown that if the Fourier transform is a bounded map on a rearrangement-invariant space of functions on $\mathbb R^n$, modified by a weight, then the weight is bounded above and below and the space is equivalent to $L^2$. Also, if it…
In this paper, we generalize and investigate Bohr-Rogosinski's inequalities and the Bohr-Rogosinski phenomenon for the subfamilies of univalent (i.e., one-to-one) functions defined on unit disk $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$ which…
In this paper, we establish several new versions of Bohr-type inequalities for bounded analytic functions in the unit disk by allowing $\varphi=\{\varphi_n(r)\}^{\infty}_{n=0}$ in place of the $\{r^n\}^{\infty}_{n=0}$ in the power series…
We study relations between subsets of integers that are large, where large can be interpreted in terms of size (such as a set of positive upper density or a set with bounded gaps) or in terms of additive structure (such as a Bohr set). Bohr…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…