Abstract
Compact operators are introduced, and in the self-adjoint case the existence of an orthonormal basis of eigenvectors is shown. This is applied to the Sturm-Liouville equation and Trace-class operators are introduced. These results are used to show the existence of a basis of eigenfunctions for the Laplace operator for a bounded domain and Weyl’s law for the asymptotic of the eigenvalues of the Laplacian is proven.
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Einsiedler, M., Ward, T. (2017). Compact Self-Adjoint Operators and Laplace Eigenfunctions. In: Functional Analysis, Spectral Theory, and Applications. Graduate Texts in Mathematics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-319-58540-6_6
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DOI: https://doi.org/10.1007/978-3-319-58540-6_6
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58539-0
Online ISBN: 978-3-319-58540-6
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