Expansion in the Fundamental System of Functions of the Laplace Operator
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.
KeywordsFourier Series Spectral Function Laplace Operator Fourier Coefficient Spectral Decomposition
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