Description
Book SynopsisThe book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.
Table of ContentsIntroduction: Variation and Semi-Variation; Regulated Functions; Riemann-Stieltjes Integrals; Kurzweil-Stieltjes Integral in R; Abstract Kurzweil-Stieltjes Integral: Definition and Basic Properties; Existence; Integration-by-Parts; Saks-Henstock Lemma; Convergence Theorems; Kurzweil-Stieltjes Integral as a Function of the Upper Limit; Kurzweil-Stieltjes Integral and Functional Analysis: General Forms of Continuous Linear Functionals on Some Function Spaces; Multiplication of Distributions; Generalized Ordinary Differential Equations: Linear Equations; Nonlinear Equations; Continuous Dependence of Solutions on a Parameter; Differential Equations with Impulses; Dynamic Equations on Time-Scales; Functional Differential Equations;
