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Smooth Cantor functions

T. W. Körner (2007)

Colloquium Mathematicae

We characterise the set on which an infinitely differentiable function can be locally polynomial.

Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Diethelm, Kai (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.

Sobolev inequalities for probability measures on the real line

F. Barthe, C. Roberto (2003)

Studia Mathematica

We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow....

Sobre la concavidad de t-normas y de funciones triangulares.

Núria Agell (1984)

Stochastica

In this note we prove that the unique concave t-norm is Minimum and, among the class of triangular functions that have the family of unit step-functions as idempotent elements, the unique concave triangular function is piM.

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