41 citations · 179 across the 30 of their papers we have counts for
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Damping estimates for oscillatory integral operators with finite type singularities
Andrew Comech
We derive damping estimates and asymptotics of operator norms for oscillatory integral operators with finite type singularities. The methods are based on incorporating finite…
Optimal regularity of Fourier integral operators with one-sided folds
Andrew Comech
We obtain optimal continuity in Sobolev spaces for the Fourier integral operators associated to singular canonical relations, when one of the two projections is a Whitney fold. The…
$L\sp p$-$L\sp q$ regularity of Fourier integral operators with caustics
Andrew Comech
The caustics of Fourier integral operators are defined as caustics of the corresponding Schwartz kernels (Lagrangian distributions on ). The caustic set of the ca…
Nonlinear instability of a critical traveling wave in the generalized Korteweg -- de Vries equation
Andrew Comech, Scipio Cuccagna, Dmitry Pelinovsky
We prove the instability of a ``critical'' solitary wave of the generalized Korteweg -- de Vries equation, the one with the speed at the border between the stability and instabilit…