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Viscosity Limits for Zeroth-Order Pseudodifferential Operators
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DOI：10.1002/cpa.22072.png)
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Motivated by the work of Colin de Verdiere and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators on tori, we consider viscosity limits in which zeroth-order operators, P, are replaced by P + i nu Delta, nu > 0. By adapting the Helffer-Sjostrand theory of scattering resonances, we show that, in a complex neighbourhood of the continuous spectrum, eigenvalues of P + i nu Delta have limits as the viscosity nu goes to 0. In the simplified setting of tori, this justifies claims made in the physics literature. (c) 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
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STOCHASTIC STABILITY
RESONANCES
DENSITY
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2.7
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1.5K
被引数:
1.1W
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