Besov Wavefront Set
Claudio Dappiaggi, Paolo Rinaldi, Federico Sclavi

TL;DR
This paper introduces a new Besov wavefront set concept to analyze distribution singularities in Fourier space, providing equivalent characterizations, a multiplication criterion, and applications to hyperbolic operator singularity propagation.
Contribution
It develops a novel Besov wavefront set framework with equivalent characterizations and a generalized multiplication criterion, extending classical results and enabling propagation of singularities analysis.
Findings
Defined a Besov wavefront set in Fourier space.
Provided an equivalent pseudo-differential operator characterization.
Proved a propagation of singularities theorem for hyperbolic operators.
Abstract
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent characterization of such wavefront set using the language of pseudo-differential operators. Both formulations are used to prove the main underlying structural properties. Among these we highlight the individuation of a sufficient criterion to multiply distributions with a prescribed Besov wavefront set which encompasses and generalizes the classical Young's theorem. At last, as an application of this new framework we prove a theorem of propagation of singularities for a large class of hyperbolic operators.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical Analysis and Transform Methods · Advanced Mathematical Physics Problems
