Correction to: Analytic orbit theory with any arbitrary spherical harmonic as the dominant perturbation

Harmonic Analysis as found in Analytic Number Theory

A wide variety of questions of Harmonic Analysis arise naturally in various contexts of Analytic Number Theory; in what follows we consider a number of examples of this type. The author is grateful to Dr. Ulrike Vorhauer for advice and assistance at all stages of preparation of this paper.

Relative Perturbation Theory for Diagonally Dominant Matrices

OF DISSERTATION RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well condi...

Analytic Equation of State for the Square-well Plus Sutherland Fluid from Perturbation Theory

Analytic expressions were derived for the compressibility factor and residual internal energy of the square-well plus Sutherland fluid. In this derivation, we used the second order Barker-Henderson perturbation theory based on the macroscopic compressibility approximation together with an analytical expression for radial distribution function of the reference hard sphere fluid. These properties...

Resummation Approach in QCD Analytic Perturbation Theory

We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar g φ4 model. Then we give a short historic preamble of APT and show that renormgroup improvement of the QCD perturbation theory dictates to use the Fractional APT (FAPT). After that we discuss the (F)APT resummation o...

Analytic Perturbation Theory and Its Applications