Functional Analysis and Applications Seminar


(organized by the Functional Analysis and Applications Group)


Department of Mathematics, University of Aveiro




Next talk of the Seminar (11:10, Room Sousa Pinto):


14/12/2017: "Generalizations of the Fourier Transform"

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. Tuan.



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.



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