Degenerate Oscillatory Integral Operators

Lead Research Organisation: University of Edinburgh
Department Name: Sch of Mathematics

Abstract

In recent years, Fourier Analysis on Euclidean Spaces has become an extremely active research area in the USA and Europe and many of the centralproblems in this area can be reduced to understanding various oscillatory integral operators. The underlying geometry of the problemoften makes the corresponding operator degenerate in a certain sense. In thisproject we aim to explore and understand degenerateoscillatory integral operators which arise in keyresearch areas.

Publications


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CARBERY A (2008) Averages in vector spaces over finite fields in Mathematical Proceedings of the Cambridge Philosophical Society

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Dendrinos S (2009) Universal in Journal of Functional Analysis

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Dendrinos S (2008) Fourier restriction, polynomial curves and a geometric inequality in Comptes Rendus Mathematique

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Dendrinos S (2010) An affine-invariant inequality for rational functions and applications in harmonic analysis in Proceedings of the Edinburgh Mathematical Society

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Folch-Gabayet M (2008) Singular integral operators associated to curves with rational components in Transactions of the American Mathematical Society

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Jones R (2008) Strong variational and jump inequalities in harmonic analysis in Transactions of the American Mathematical Society

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LAGHI N (2008) A note on restricted X-ray transforms in Mathematical Proceedings of the Cambridge Philosophical Society

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Oberlin R (2012) A variation norm Carleson theorem in Journal of the European Mathematical Society