Baire's Space of Permutations of n and Rearrangements of Series
Banach algebra techniques in the theory of arithmetic functions
For infinite discrete additive semigroups we study normed algebras of arithmetic functions endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.
Banach and statistical cores of bounded sequences
In this paper, we are mainly concerned with characterizing matrices that map every bounded sequence into one whose Banach core is a subset of the statistical core of the original sequence.
Basilejský problém devětkrát jinak
V tomto článku podrobně rozebereme celkem devět řešení tzv. basilejského problému (hledání součtu převrácených hodnot druhých mocnin přirozených čísel). První publikované řešení od L. Eulera využívá rozkladu ``nekonečného polynomu'' na součin kořenových činitelů. Druhé řešení pracuje s Taylorovým rozvojem funkce arkussinus a rekurentním vzorcem pro jistý určitý integrál, třetí je založeno na vztazích mezi goniometrickými funkcemi a exponenciálou a výpočtu limity s využitím l'Hospitalova pravidla....
Beiträge zur Theorie der durch die Heinesche Reihe: ... darstellbaren Functionen.
Bemerkung über trigonometrische Reihen
Bemerkungen über Kettenbrüche.
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