Heat Kernel for a Generalized Ornstein-Uhlenbeck operator
碩士 === 國立清華大學 === 數學系 === 102 === In this thesis, we use the Hamiltonian and Lagrangian formalism to study the two-dimensional generalized Ornstein-Uhlenbeck operator Given the boundary conditions, we find the solutions of the associated Hamiltonian system of this operator. Then we construct the act...
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| Format: | Others |
| Language: | en_US |
| Published: |
2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/68532732337275517749 |
| Summary: | 碩士 === 國立清華大學 === 數學系 === 102 === In this thesis, we use the Hamiltonian and Lagrangian formalism to study the two-dimensional generalized Ornstein-Uhlenbeck operator Given the boundary conditions, we find the solutions of the associated Hamiltonian system of this operator. Then we construct the action function by the Lagrangian function and use the van Vleck's formula to obtain the volume element of the heat kernel. Finally, we discuss the regular and singular regions of this operator.
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