Spectral Theory

  • Michael E. Taylor
Part of the Applied Mathematical Sciences book series (AMS, volume 116)


This chapter is devoted to the spectral theory of self-adjoint, differential operators. We cover a number of different topics, beginning in §1 with a proof of the spectral theorem. It was an arbitrary choice to put that material here, rather than in Appendix A, on functional analysis. The main motivation for putting it here is to begin a line of reasoning that will be continued in subsequent sections, using the great power of studying unitary groups as a tool in spectral theory. After we show how easily this study leads to a proof of the spectral theorem in §1, in later sections we use it in various ways: as a tool to establish self-adjointness, as a tool for obtaining specific formulas, including basic identities among special functions, and in other capacities.


Laplace Operator Dirichlet Boundary Condition Neumann Boundary Condition Diffract Wave Integral Kernel 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillUSA

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