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Boundary value problems and spectral geometry is an attractive and rapidly developing area in modern mathematical analysis. The interaction of PDE methods with concepts from operator theory and differential geometry is particularly challenging and leads directly to new insights and applications in various branches of pure and applied mathematics, e.g., analysis on manifolds, global analysis and mathematical physics. Some recent contributions in the field of boundary value problems and spectral geometry concern, e.g., construction of isospectral manifolds with boundary, eigenvalue and resonance distribution for large energies, multidimensional inverse spectral problems, singular perturbations, new regularity techniques, Dirichletto-Neumann maps and Titchmarsh-Weyl functions.
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Jussi Behrndt, Konstantin Pankrashkin, Olaf Post, Mini-Workshop: Boundary Value Problems and Spectral Geometry. Oberwolfach Rep. 9 (2012), no. 1, pp. 43–76DOI 10.4171/OWR/2012/02