Advertisement

Expansion in the Fundamental System of Functions of the Laplace Operator

  • V. A. Il’in

Abstract

In this chapter, we introduce the concept of a fundamental system of functions (FSF) for the simplest elliptic operator, the Laplace operator, defined in an arbitrary (not necessarily bounded) N-dimensional domain. The FSF encompasses the eigenfunction systems of all self-adjoint boundary-value problems for the Laplace operator; for such systems, the spectrum is a pure point spectrum, admitting of an infinite multiplicity and every where dense set of limit points for the eigenvalues — quite a realistic situation, as we shall see later.

Keywords

Fourier Series Spectral Function Laplace Operator Fourier Coefficient Spectral Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Consultants Bureau 1995

Authors and Affiliations

  • V. A. Il’in
    • 1
  1. 1.Moscow State UniversityMoscowRussia

Personalised recommendations