Next talk of the Seminar (11:10, Room Sousa Pinto):
14/12/2017: "Generalizations of the
Luís Castro (CIDMA – Center
for Research and Development in Mathematics and Applications, Department of
Mathematics, University of Aveiro)
We will introduce
some generalizations of the Fourier transform which can also be seen as
generalizations of the so-called linear canonical transform. Operational
and fundamental properties of those integral transforms 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 generalizations 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 certain quadratic-phase Fourier oscillatory integral operator
will be analysed. The talk is based on joint work with L.T. Minh and N.M.
This Seminar is supported in part by the
Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia),
through CIDMA - Center for Research and Development in Mathematics and
Applications, within project UID/MAT/04106/2013.