English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove a Plancherel theorem for a nonlinear Fourier transform in twodimensions arising in the Inverse Scattering method for the defocusingDavey-Stewartson II equation. We then use it to prove global well-posedness andscattering in $L^2$ for defocusing DSII. This Plancherel theorem also impliesglobal uniqueness in the inverse boundary value problem of Calder\'on indimension $2$, for conductivities $\sigma>0$ with $\log \sigma \in \dot H^1$.The proof of the nonlinear Plancherel theorem includes new estimates onclassical fractional integrals, as well as a new result on $L^2$-boundedness ofpseudo-differential operators with non-smooth symbols, valid in all dimensions.

A Nonlinear Plancherel Theorem with Applications to Global  Well-Posedness for the Defocusing Davey-Stewartson Equation and to the  Inverse Boundary Value Problem of Calder\'on