Oscillatory and Fourier integral operators with degenerate canonical relations

By Allan Greenleaf, Andreas Seeger. 2002

48 citations recorded by the source corpus.

We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors. [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fea2e7a7bd66790319b860083433516bbfaac2c1

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

L p IMPROVING BOUNDS FOR AVERAGES ALONG CURVES (2001, background): “For the restricted x-ray transformRn above, ~1 has only singularities that belong to the Morin singularity classesS1k;0; 1 k n 3 (see [ 15 ] for a discussion of these singularity classes and their connections with the operators considered here), while both projections ~1 and ~2 for the convolution e”
Multilinear generalized Radon transforms and point configurations (2012, background): “Beyond their original role in integral geometry, generalized Radon transforms and their singular variants have since become ubiquitous in harmonic analysis, partial differential equations and related areas [34, 35, 36, 37, 15], and more recently as tools to study geometric and combinatorial problems”
A multi-dimensional resolution of singularities with applications to analysis (2010, background): “8], [53, 54, 10, 11, 31]), while their operator analogues are central to the study of regularity properties of Fourier integral operators [42, 48, 47, 14, 23].”
Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “In the situation where d = d we refer the reader to [32] for a survey of a variety of results relating to L(2) bounds in the situation where the condition (5.”