Related papers: On the Bohr phenomenon for complex valued and vect…
A conformal factor in the Bohr model embeds Bohr space in six dimensions, revealing the $O(6)$ symmetry and its contraction to the $E(5)$ at infinity. Phenomenological consequences are discussed after the re-formulation of the Bohr…
A thorough analysis is made of the Fourier coefficients for vector-valued modular forms associated to three-dimensional irreducible representations of the modular group. In particular, the following statement is verified for all but a…
A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…
We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions. As an application we give a very explicit description of…
We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional…
This paper investigates the relation between the Fourier transform of {\rm BV} (bounded variation) functions and their jump sets. We introduce the notion of $L^2$-jump product and obtain a weighted Plancherel identity for {\rm BV}…
Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same…
We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded…
The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…
In this paper, we investigates the Bohr phenomenon for holomorphic mappings $F$ from the unit ball $\mathbb{B}_X$ of a complex Banach space $X$ into the closure of the unit polydisc $\mathbb{D}^m$ within the space $\mathbb{C}^m$. First, we…
The classical inequality of Bohr concerning Taylor coeficients of bounded holomorphic functions on the unit disk, has proved to be of significance in answering in the negative the conjecture that if the non-unital von Neumann inequality…
In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in $\mathbb{C}^n$ under some restricted conditions. Next, we determine the refined version of…
We introduce and study weighted spaces of functions with mixed norm on the upper half-plane, defined in terms of Fourier transform. We give a characterization of analytic functions within these spaces, and in particular, we provide an…
Recently the present authors established refined versions of Bohr's inequality in the case of bounded analytic functions. In this article, we state and prove a generalization of these results in a reformulated "distance form" version and…
The main purpose of this paper is to study the validity of the Hausdorff-Young inequality for vector-valued functions defined on a non-commutative compact group. The natural context for this research is that of operator spaces. This leads…
We examine the problem of the Fourier transform mapping one weighted Lebesgue space into another, by studying necessary conditions and sufficient conditions which expose an underlying geometry. In the necessary conditions, this geometry is…
This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.
This note contains two simple observations. First, by the weak factorization of product $H^1$ (Ferguson--Lacey, Lacey--Terwilleger), we obtain a multi-parameter analogue of Hardy's inequality. Second, as a dual statement, the Fourier…
The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given…
Spectral Barron spaces, which quantify the absolute value of weighted Fourier coefficients of a function, have gained considerable attention due to their capability for universal approximation across certain function classes. By…