Introduction

Abstract

Already in Chap. 20 on p. 229, we have encountered the concept of an eigenvalue problem, although in a brief form only. In the conception of this book based on the theory of the Hilbert space, the following preliminary formulation of the eigenvalue problem is possible¹): Let A be a linear operator in a Hilbert space H (defined, possibly, only on some linear set from this space). The number λ is called an eigenvalue of this operator if there exists a nonzero element u ∈ H such that in H we have

$$Au - \lambda u = 0.$$

(37.1)

The element u is called the eigenelement of the operator A (frequently also the eigenelement of the equation (37.1)) corresponding to the eigenvalue λ.