Partial Differential Equations
Chapman & Hall/CRC (Verlag)
978-1-032-07409-2 (ISBN)
Using Fourier analysis, the text constructs explicit formulas for solving PDEs governed by canonical operators related to the Laplacian on the Euclidean space. After presenting background material, it focuses on: Second-order equations governed by the Laplacian on Rn; the Hermite operator and corresponding equation; and the sub-Laplacian on the Heisenberg group
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. Through its coverage of fundamental examples of PDEs, the book prepares students for studying more advanced topics such as pseudo-differential operators. It also helps them appreciate PDEs as beautiful structures in analysis, rather than a bunch of isolated ad-hoc techniques.
New to the Second Edition
Three brand new chapters covering several topics in analysis not explored in the first edition
Complete revision of the text to correct errors, remove redundancies, and update outdated material
Expanded references and bibliography
New and revised exercises.
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).
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.
| Erscheinungsdatum | 22.08.2024 |
|---|---|
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 385 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Technik ► Umwelttechnik / Biotechnologie | |
| ISBN-10 | 1-032-07409-4 / 1032074094 |
| ISBN-13 | 978-1-032-07409-2 / 9781032074092 |
| Zustand | Neuware |
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