Partial differential equations : topics in Fourier analysis


Partial differential equations : topics in Fourier analysis

M. W. Wong

(A Chapman & Hall book)

CRC Press, c2023

Second edition

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Includes bibliographical references (p. 191-194) and index



New to the Second Edition Complete revision of the text to correct errors, remove redundancies, and update outdated material Expanded references and bibliography New and revised exercises Three brand new chapters covering several topics in analysis not explored in the first edition.


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.

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