Derives semi-classical asymptotics for the heat kernel of the ar{ar{ heta}}-Neumann Laplacian on complex manifolds with boundary as k to infinity, extending Bismut, and applies to Morse inequalities and a Weyl law.
Davies, Spectral Theory and Differential Operators, Cambridge University Press
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A spectral basis truncation in space and quadrature in time is analyzed for approximating fractional stochastic evolution equations, with strong error bounds proved and verified numerically.
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Semi-classical heat kernel asymptotics on complex manifolds with boundary
Derives semi-classical asymptotics for the heat kernel of the ar{ar{ heta}}-Neumann Laplacian on complex manifolds with boundary as k to infinity, extending Bismut, and applies to Morse inequalities and a Weyl law.
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Spectral approximation of a new class of stochastic fractional evolution equations
A spectral basis truncation in space and quadrature in time is analyzed for approximating fractional stochastic evolution equations, with strong error bounds proved and verified numerically.