The Hilbert transform of a function g, H(g) is an important tool in many mathematical fields. Expecially its numerical evaluation is often useful in some procedures for searcing solutions of the singular integral equations. In this context an approximation of (HV^alpha,beta,f;t), |t|1, where f is a continuous function in [-1,1] and v^alpha,beta, alpha,beta>-1 is a Jacobi weight, is required. In the last decade more then one paper appeared on this subject and among others we recall [1,2,3,4,5,14,15,20]. The procedure used in these papers can be described as follows.

General classes of two variables Appell polynomials are introduced by exploiting properties of an iterated isomorphism, related to the so-called Laguerre-type exponentials. Further extensions to the multi-index and multivariable cases are mentioned. (C) 2004 Elsevier Ltd. All rights reserved.

In this paper we analyze the performance of the three MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) observation modes that sound the Upper-Troposphere/Lower-Stratosphere (UT/LS) region. The two-dimensional (2-D) tomographic retrieval approach is assumed to derive the atmospheric field of geophysical parameters. For each observation mode we have calculated the 2-D distribution of the information load quantifier relative to the main MIPAS targets.

The work deals the monitoring of a single ancient landslide detected in the Vonace area, southwards of Maierato (Calabria, Italy). A 18-hour-measurement campaign has been carried out using the Ground-based Synthetic Aperture Radar (GBSAR) interferometry technique carried between March, 25th and 26th. Displacement maps have been geolocated and overlaid to a Digital Elevation Model of the scene. It has been observed that the Vonace area is almost stable except two portions located at the foot of the ancient landslide and at the centre of the town, respectively.