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About the generating function of a left bounded integer-valued random variable

Charles Delorme, Jean-Marc Rinkel (2008)

Bulletin de la Société Mathématique de France

We give a relation between the sign of the mean of an integer-valued, left bounded, random variable X and the number of zeros of 1 - Φ ( z ) inside the unit disk, where Φ is the generating function of X , under some mild conditions

Abstract inclusions in Banach spaces with boundary conditions of periodic type

Lahcene Guedda, Ahmed Hallouz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ x S ( x ( 0 ) , s e l F ( x ) ) ⎨ ⎩ x (T) = x(0), where, F : [ 0 , T ] × 2 E is a multivalued map with convex compact values, ⊂ E, s e l F is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive...

Accelero-summation of the formal solutions of nonlinear difference equations

Geertrui Klara Immink (2011)

Annales de l’institut Fourier

In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level 1 + ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...

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