M. W. Wong

Partial Differential Equations (eBook, PDF)

Topics in Fourier Analysis

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 208
• Erscheinungstermin: 19. August 2022
• Englisch
• ISBN-13: 9781000636802
• Artikelnr.: 64244172

Autorenporträt

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).

Inhaltsangabe

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.