Related papers: Bohr's Theorem for Monogenic Power Series

The main aim of this paper is to establish several Landau-type theorems for certain bounded poly-analytic functions and reduced poly-analytic functions that generalize some previously established results.

In the paper [1] we consider a new class, so-called, $G$-monogenic (differentiable in the sense of Gateaux) quaternionic mappings. In the present paper we introduce quaternionic $H$-monogenic (differentiable in the sense of Hausdorff)…

We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…

In this paper, we provide a new method to find all zeros of polynomials with quaternionic coefficients located on only one side of the powers of the variable (these polynomials are called simple polynomials). This method is much more…

The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of ``A General Geometric Fourier Transform`` in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which…

This paper is a short introduction to orthogonal polynomials, both the general theory and some special classes. It ends with some remarks about the usage of computer algebra for this theory.

We generalize Barr's embedding theorem for regular categories to the context of enriched categories.

For real power series whose non-zero coefficients satisfy $|a_m|^{1/m}\to~1$ we prove a stronger version of Fabry theorem relating the frequency of sign changes in the coefficients and analytic continuation of the sum of the power series.

Basing on the Bohr collective quadrupole Hamiltonian the $A$-dependence of the Grodzins product is derived and the proportionality coefficient for the Grodzins relation is evaluated. The result obtained is in a correspondence with the…

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

This article focuses on the Bohr radius problem for the derivatives of analytic functions, along with a technique of establishing Bohr inequalities in classical and generalized settings.

Let $ \mathcal{B}:=\{f(z)=\sum_{n=0}^{\infty}a_nz^n\; \mbox{with}\; |f(z)|<1\;\mbox{for all}\; z\in\mathbb{D}\} $. The improved version of the classical Bohr's inequality \cite{Bohr-1914} states that if $ f\in\mathcal{B} $, then the…

In this article, we investigate Bohm's view of quantum theory, especially Bohm's quantum potential, from a new perspective. We develop a quasi-Newtonian approach to Bohmian mechanics. We show that to arrive at Bohmian formulation of quantum…

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of…

In this paper we present a perturbation theory for constant quaternionic potentials. The effects of quaternionic perturbations are explicitly treated for bound states of hydrogen atom, infinite potential well and harmonic oscillator.…

Using convexity and superquadracity we extend in this paper Euler Lagrange identity, Bohr's inequalitiy and the triangle inequality.

The main aim of this article is to establish a sharp improvement of the classical Bohr inequality for bounded holomorphic mappings in the polydisk $\mathbb{P}\Delta(0;1_n)$. We also prove two other sharp versions of the Bohr inequality in…

In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic…

In this paper, we study the Bohr inequality with lacunary series to the single valued (resp. vector-valued) holomorphic function defined in unit ball of finite dimensional Banach sequence space. Also, we extend the Bohr inequality with an…

We discuss the Schrodinger equation in presence of quaternionic potentials. The study is performed analytically as long as it proves possible, when not, we resort to numerical calculations. The results obtained could be useful to…