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RESEARCH PRODUCT

Distribution of Large Eigenvalues for Elliptic Operators

Johannes Sjöstrand

subject

symbols.namesakePure mathematicsElliptic operatorDistribution (mathematics)Weyl lawPoincaré conjecturesymbolsAlmost surelyDifferential operatorEigenvalues and eigenvectorsManifoldMathematics

description

In this chapter we consider elliptic differential operators on a compact manifold and rather than taking the semi-classical limit (h →), we let h = 1 and study the distribution of large eigenvalues. Bordeaux Montrieux (Loi de Weyl presque sure et resolvante pour des operateurs differentiels non-autoadjoints, these, CMLS, Ecole Polytechnique, 2008. https://pastel.archives-ouvertes.fr/pastel-00005367, Ann Henri Poincare 12:173–204, 2011) studied elliptic systems of differential operators on S1 with random perturbations of the coefficients, and under some additional assumptions, he showed that the large eigenvalues obey the Weyl law almost surely. His analysis was based on a reduction to the semi-classical case, where he could use and extend the methods of Hager (Ann Henri Poincare 7:1035–1064, 2006).

yearjournalcountryeditionlanguage
2019-01-01
https://doi.org/10.1007/978-3-030-10819-9_18