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Expansion in the Fundamental System of Functions of the Laplace Operator

In: Spectral Theory of Differential Operators

Author

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  • V. A. Il’in

    (Moscow State University)

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.

Suggested Citation

  • V. A. Il’in, 1995. "Expansion in the Fundamental System of Functions of the Laplace Operator," Springer Books, in: Spectral Theory of Differential Operators, chapter 0, pages 1-81, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1755-9_1
    DOI: 10.1007/978-1-4615-1755-9_1
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