The Bohr inequality for ordinary Dirichlet series

Bohr and Rogosinski Abscissas for Ordinary Dirichlet Series

We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain G ⊂ C are independent of the domain G. Furthermore, we obtain new estimates about these abscissas. 1. Preliminaries Let us recall the theorem of H.Bohr [19] in 1914. Theorem 1.1. If a power series

Cesàro Summability of Ordinary Double Dirichlet Series

Generalization of Caratheodory’s Inequality and the Bohr Radius for Multidimensional Power Series

Matrix Order in Bohr Inequality for Operators

The classical Bohr inequality says that |a+b| ≤ p|a|+q|b| for all scalars a, b and p, q > 0 with 1 p + 1 q = 1. The equality holds if and only if (p− 1)a = b. Several authors discussed operator version of Bohr inequality. In this paper, we give a unified proof to operator generalizations of Bohr inequality. One viewpoint of ours is a matrix inequality, and the other is a generalized parallelogr...

Analytical D’Alembert Series Solution for Multi-Layered One-Dimensional Elastic Wave Propagation with the Use of General Dirichlet Series

A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...