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Positively homogeneous functions and the Łojasiewicz gradient inequality

Alain Haraux (2005)

Annales Polonici Mathematici

It is quite natural to conjecture that a positively homogeneous function with degree d ≥ 2 on ℝ N satisfies the Łojasiewicz gradient inequality with exponent θ = 1/d without any need for an analyticity assumption. We show that this property is true under some additional hypotheses, but not always, even for N = 2.

Prevalence of "nowhere analyticity"

Françoise Bastin, Céline Esser, Samuel Nicolay (2012)

Studia Mathematica

This note brings a complement to the study of genericity of functions which are nowhere analytic mainly in a measure-theoretic sense. We extend this study to Gevrey classes of functions.

Principe de la phase résonnante

Jacques Vey (1979)

Annales de l'institut Fourier

On donne une variante du principe de la phase stationnaire, où l’intégrale est remplacée par une sommation sur le réseau cubique de maille égale à l’unité de phase.

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