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

In this paper, we furnish van der Corput types estimates for oscillatoryintegrals with respect to a large parameter, where the phase is allowed to havea stationary point of real order and the amplitude to have an integrablesingularity. The resulting estimates show explicitly the influence of these twoparticular points on the decay. These results are then applied to the solutionsof a family of dispersive equations whose generators are Fourier multipliers.We explore the effect of a limitation to compact frequency bands and ofsingular frequencies of the initial condition on the decay. Uniform estimatesin space-time cones as well as L-infinity-norm estimates are furnished and theoptimality of the decay rates is proved under certain hypotheses. Moreover theinfluence of a growth limitation at infinity of the symbols on the dispersionis exhibited.

Asymptotic estimates of oscillatory integrals with general phase and singular amplitude: Applications to dispersive equations