Partial Differential Equations: Topics in Fourier Analysis

by M. W. Wong

Overview

Designed for a one-semester course, this text provides a bridge between the standard PDE course for undergraduate students in science and engineering and the PDE course for graduate students in mathematics who are pursuing a research career in analysis.

Product Details

ISBN-13:	9781032074092
Publisher:	CRC Press
Publication date:	08/26/2024
Edition description:	2nd ed.
Pages:	208
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

M. W. Wong is a professor in and former chair of the Department of Mathematics and Statistics at York University in Toronto, Canada. From 2005 to 2009, he was president of the International Society for Analysis, its Applications and Computations (ISAAC).

Table of Contents

1. The Multi-Index Notation. 2. The Gamma Function. 3. Convolutions. 4. Fourier Transforms. 5. Tempered Distributions. 6. The Heat Kernel. 7. The Free Propagator. 8. The Newtonian Potential. 9. The Bessel Potential. 10. Global Hypoellipticity in the Schwartz Space. 11. The Poisson Kernel. 12. The Bessel–Poisson Kernel. 13. Wave Kernels. 14. The Heat Kernel of the Hermite Operator. 15. The Green Function of the Hermite Operator. 16. Global Regularity of the Hermite Operator. 17. The Heisenberg Group. 18. The Sub-Laplacian and the Twisted Laplacians. 19. Convolutions on the Heisenberg Group. 20. Wigner Transforms and Weyl Transforms. 21. Spectral Analysis of Twisted Laplacians. 22. Heat Kernels Related to the Heisenberg Group. 23. Green Functions Related to the Heisenberg Group. 24. Theta Functions and the Riemann Zeta-Function. 25. The Twisted Bi-Laplacian. 26. Complex Powers of the Twisted Bi-Laplacian. Bibliography. Index.