Operators and Functionals, especially in Hilbert Spaces

Abstract

In the sequel, equations of the form

$$Au = f$$

(8.1)

will be considered, where A is a certain operator (in applications a differential operator most frequently), f is a given element (as a rule, a function considered as an element of a Hilbert space, e.g., of the space L₂(G)), and u is the desired solution. To explain the meaning of equation (8.1) in more detail let us present a simple example.