A Brief Introduction to Hilbert Space and Quantum logic

Abstract

The purpose of this paper is to describe some applications of the theory of Hilbert spaces to integral equations. The main goal is to illustrate possible applications of techniques developed in theory and to include the standard classification of the important integral equations (Volterra,Fredholm, Integro-Differential, Singular and Abel s integral equations) and their solvability. The most available methods of the subject are abstract and most of them are based on comprehensive theories such as topological methods of functional analysis. This paper uses some recent developments in the solution of integral equations without using the extensive mathematical theory and leaves out abstract and comprehensive methods. The main goal of this paper is to provide both a systematic exposition of the basic ideas and resultsof Hilbert space theory and functional analysis, and an introduction to various methods of solution of integral equations. Several examples with solutions are introduced in each section.