Analysis of Meromorphic Functions and Integral Transforms

The analysis of many physical phenomena often calls for the detection and characterization of the complex poles of certain mathematical structures. For instance, the poles of the S-matrix for the analysis of resonances and echoes in nuclear and sub-nuclear physics, the poles of the transfer function in system analysis, the poles of the complex conductivity distribution in Electric Impedance Tomography. Moreover, these mathematical structures are ususlly associated with suitable integral transforms, e.g., the Laplace transform in system analysis, the Abel-Radon transform in tomography. The first purpose of this study is the theoretical characterization of the poles (and of the related residues) associated with classes of meromorphic functions which are of physical interest. In particular, the focus is on those classes which can be representated as the integral transform of suitable functions. Secondly, from this theoretical analysis we aim at defining and implmenting numerical algorithms for the detection and characterization of complex poles from signals, and for stating numerical procedures for the effective inversion of certain integral transforms.

Members:
Enrico De Micheli (Principal investigator)