15/09/2016, 14:55 — 15:45 — Room 6.2.38, Faculty of Sciences of the Universidade de Lisboa
Luís Castro, Universidade de Aveiro
Quadratic-phase Fourier transform
We will introduce a generalization of the Fourier transform that can also be seen as a generalization of the so-called linear canonical transform. Some of its operational and fundamental properties will be studied. This includes a Riemann-Lebesgue type lemma, invertibility results, a Plancherel type theorem and a Parseval type identity. Moreover, several new convolutions associated with the introduced transform are obtained. The applicability of those convolutions (containing weight-functions related to some amplitude and Gaussian functions) will be briefly illustrated by solving a class of integral equations. In addition, the norm decay rate of the corresponding quadratic-phase Fourier oscillatory integral operator will be analysed. The talk is based on joint work with N.M. Tuan.
