Best order conditions in linear spaces, with applications to limitation, inclusion and high indices theorems for ordinary and absolute Riesz means
Best Possible Bounds and Monotonicity of Segments of Harmonic Series (II)
Book Reviews
Borel matrix
We study the Borel summation method. We obtain a general sufficient condition for a given matrix to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the -setting, we establish necessary conditions of the same kind by using Bourgain’s...
Borel summability beyond the factorial growth
Borel summation and splitting of separatrices for the Hénon map
We study two complex invariant manifolds associated with the parabolic fixed point of the area-preserving Hénon map. A single formal power series corresponds to both of them. The Borel transform of the formal series defines an analytic germ. We explore the Riemann surface and singularities of its analytic continuation. In particular we give a complete description of the “first” singularity and prove that a constant, which describes the splitting of the invariant manifolds, does not vanish. An interpretation...
Boundary behavior and Cesàro means of universal Taylor series.
We study boundary properties of universal Taylor series. We prove that if f is a universal Taylor series on the open unit disk, then there exists a residual subset G of the unit circle such that f is unbounded on all radii with endpoints in G. We also study the effect of summability methods on universal Taylor series. In particular, we show that a Taylor series is universal if and only if its Cesàro means are universal.
Bounded analytic functions in the unit disk and the behaviour of certain analytic continued fractions near singular line.
Bounded index, entire solutions of ordinary differential equations and summability methods.
Bounded variation sequences of order k and the representation of null sequences.
Boundness of Cesàro means operators.
Brève communication. Transformations de suites
Calculations in new sequence spaces
In this paper we define new sequence spaces using the concepts of strong summability and boundedness of index of -th order difference sequences. We establish sufficient conditions for these spaces to reduce to certain spaces of null and bounded sequences.
Calculations on some sequence spaces.
Capacity of Sets and Uniform Distribution of Sequences.
Caractère de convergence des séries
Cesàro statistical core of complex number sequences.
Cesàro summability factors and a comparison of convergence rates
Cesàro wedge and weak Cesàro wedge -spaces
In this paper we deal with Cesàro wedge and weak Cesàro wedge -spaces, and give several characterizations. Some applications of these spaces to general summability domains are also studied.
Chapitre VII. Démonstration du théorème fondamental