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Composition of some singular Fourier integral operators and estimates for restricted X -ray transforms

Allan Greenleaf, Gunther Uhlmann (1990)

Annales de l'institut Fourier

We establish a composition calculus for Fourier integral operators associated with a class of smooth canonical relations C ( T * X 0 ) × ( T * Y 0 ) . These canonical relations, which arise naturally in integral geometry, are such that π : C T * Y is a Whitney fold and ρ : C T * X is a blow-down mapping. If A I m ( C ) , B I m ' ( C t ) , then B A I m + m ' , 0 ( Δ , Λ ) a class of pseudodifferential operators with singular symbols. From this follows L 2 boundedness of A with a loss of 1/4 derivative.

Courbures intrinsèques dans les catégories analytico-géométriques

Andreas Bernig, Ludwig Bröcker (2003)

Annales de l’institut Fourier

Deux types de courbures sont associés à un sous-ensemble compact et définissable d'une variété riemannienne analytique réelle. Si la variété est de courbure constante, il y a des relations linéaires entre ces mesures. Comme application, nous démontrons une formule cinématique, définissons des densités locales, et nous étudions les volumes des simplexes réguliers.

Curvature bounds for neighborhoods of self-similar sets

Steffen Winter (2011)

Commentationes Mathematicae Universitatis Carolinae

In some recent work, fractal curvatures C k f ( F ) and fractal curvature measures C k f ( F , · ) , k = 0 , ... , d , have been determined for all self-similar sets F in d , for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations...

Density of a family of linear varietes

Grazia Raguso, Luigia Rella (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The measurability of the family, made up of the family of plane pairs and the family of lines in 3 -dimensional space A 3 , is stated and its density is given.

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