Seminars Oscillatory Integrals

Period of duration of course
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Course info
Number of course hours
20
Number of hours of lecturers of reference
20
Number of hours of supplementary teaching
0
CFU 3
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Modalità esame

Seminars

Lecturer

View lecturer details

Lecturer

Gian Maria Dall'Ara

Prerequisiti

Elements of Fourier Analysis on Euclidean Spaces.

Programma

Asymptotics of oscillatory integrals via resolution of singularities. Van der Corput-type estimates, sublevel set lemmas and the issue of stability. Depending on time and interest, I also want to talk about recent developments and applications.

Obiettivi formativi

Learn various classical and modern techniques for bounding and finding asymptotics of oscillatory integrals and oscillatory integral operators, with a view toward applications to harmonic analysis, PDEs etc.

Riferimenti bibliografici

I will use various sources, among them: E. M. Stein, Harmonic Analysis; G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov Trigonometric Sums in Number Theory and Analysis; V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko Singularities of Differentiable Maps, Vol. 2.

E-mail: gianmaria.dallara@sns.it