Heat Kernels for Elliptic and Sub-elliptic Operators

1. Introduction
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

2. A Brief Introduction to the Calculus of Variations
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

3. The Geometric Method
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

4. Commuting Operators
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

5. The Fourier Transform Method
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

6. The Eigenfunction Expansion Method
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

7. The Path Integral Approach
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

8. The Stochastic Analysis Method
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

9. Laplacians and Sub-Laplacians
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

10. Heat Kernels for Laplacians and Step-2 Sub-Laplacians
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

11. Heat Kernel for the Sub-Laplacian on the Sphere S
3

Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

12. Finding Heat Kernels Using the Laguerre Calculus
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

13. Constructing Heat Kernels for Degenerate Elliptic Operators
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

14. Heat Kernel for the Kohn Laplacian on the Heisenberg Group
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

15. The Pseudo-Differential Operator Technique
Ovidiu Calin, Der-Chen Chang, Kenro Furutani, Chisato Iwasaki

Keywords: Mathematics, Partial Differential Equations, Mathematical Methods in Physics, Operator Theory, Differential Geometry, Probability Theory and Stochastic Processes, Abstract Harmonic Analysis