Wong M.W. Partial Differential Equations: Topics in Fourier Analysis

New York: Chapman and Hall/CRC, 2013. — 182 p.Partial Differential Equations: Topics in Fourier Analysis explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models. It shows how this powerful approach is valuable in getting plausible answers that can then be justified by modern analysis.Using Fourier analysis, the texThe Multi-Index Notation.
The Gamma Function.
Convolutions.
Fourier Transforms.
Tempered Distributions.
The Heat Kernel.
The Free Propagator.
The Newtonian Potential.
The Bessel Potential.
Global Hypoellipticity in the Schwartz Space.
The Poisson Kernel.
The Bessel-Poisson Kernel.
Wave Kernels.
The Heat Kernel of the Hermite Operator.
The Green Function of the Hermite Operator.
Global Regularity of the Hermite Operator.
The Heisenberg Group.
The Sub-Laplacian and Twisted Laplacians.
Convolutions on the Heisenberg Group.
Wigner Transforms and Weyl Transforms.
Spectral Analysis of Twisted Laplacians.
Heat Kernels Related to the Heisenberg Group.
Green Functions Related to the Heisenberg Group.