Anna Maria Minotti | Searcharxiv

arXiv2015

Approximation of discontinuous signals by sampling Kantorovich series

In this paper, the behavior of the sampling Kantorovich operators has been studied, when discontinuous signals are considered in the above sampling series. Moreover, the rate of approximation for the family of the above operators is estimated, when uniformly continuous and bounded signals are considered. Further, also the problem of the linear prediction by sampling values from the past is analyzed. At the end, the role of duration-limited kernels in the previous approximation processes has been treated, and several examples have been provided.

math.FA↗

arXiv2014

Applications of sampling Kantorovich operators to thermographic images for seismic engineering

In this paper, we present some applications of the multivariate sampling Kantorovich operators $S_w$ to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show how it is possible to approximate/reconstruct multivariate signals, such as images. In particular, to obtain applications for thermographic images a mathematical algorithm is developed using MATLAB and matrix calculus. The setting of Orlicz spaces is important since allow us to reconstruct not necessarily continuous signals by means of $S_w$. The reconstruction of thermographic images of buildings by our sampling Kantorovich algorithm allow us to obtain models for the simulation of the behavior of structures under seismic action. We analyze a real world case study in term of structural analysis and we compare the behavior of the building under seismic action using various models.

cs.CV↗

arXiv2011

Set-valued Kurzweil-Henstock Integral in Riesz spaces

A multivalued integral in Riesz spaces is given using the Kurzweil-Henstock integral construction. Some of its properties and a comparison with the Aumann approach are also investigated.

math.FA↗