Modern Trends in Pseudo-differential Operators

The ISAAC Group in Pseudo-Differential Operators (IGPDO) met at the Fifth ISAAC Congress held at Universitá di Catania in Italy in July, 2005. This volume consists of papers based on lectures given at the special session on pseudodifferential operators and invited papers that bear on the themes of IGPDO. Nineteen peer-reviewed papers represent modern trends in pseudo-differential operators. Topics include partial differential equations, global analysis, geometry, quantization, Wigner transforms, Weyl transforms on Lie groups, mathematical physics and timefrequency analysis. The articles will be of interest to graduate students and researchers in analysis, mathematical physics and mathematical sciences. This collection of essays and research articles under the banner of IGPDO is a valuable complement to the volumes "Advances in Pseudo-Differential Operators" and "Pseudo-Differential Operators and Related Topics" published in the same series in 2004 and 2006, respectively.

The quantization of edge symbols	p. 1
On rays of minimal growth for elliptic cone operators	p. 33
Symbolic calculus of pseudo-differential operators and curvature of manifolds	p. 51
Weyl transforms, heat kernels, green functions and Riemann zeta functions on compact Lie groups	p. 67
On the fourier analysis of operators on the torus	p. 87
Wave kernels of the twisted Laplacian	p. 107
Super-exponential decay of solutions to differential equations in R[superscript d]	p. 117
Gevrey local solvability for degenerate parabolic operators of higher order	p. 135
A new aspect of the L[superscript p] extension problem for inhomogeneous differential equations	p. 153
Continuity in quasi-homogeneous Sobolev spaces for pseudo-differential operators with Besov symbols	p. 161
Continuity and Schatten properties for pseudo-differential operators on modulation spaces	p. 173
Algebras of pseudo-differential operators with discontinuous symbols	p. 207
A class of quadratic time-frequency representations based on the short-time fourier transform	p. 235
A characterization of Stockwell spectra	p. 251
Exact and numerical inversion of pseudo-differential operators and applications to signal processing	p. 259
On the product of localization operators	p. 279
Gelfand-Shilov spaces, pseudo-differential operators and localization operators	p. 297
Continuity and Schatten properties for Toeplitz operators on modulation spaces	p. 313
Microlocalization within some classes of fourier hyperfunctions	p. 329
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Modern Trends in Pseudo-differential Operators

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