Expansion in the Fundamental System of Functions of the Laplace Operator

V. A. Il’in
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V. A. Il’in: Moscow State University

Chapter Chapter 1 in Spectral Theory of Differential Operators, 1995, pp 1-81 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-1755-9_1

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DOI: 10.1007/978-1-4615-1755-9_1

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