An ordered set of Nörlund means.
Analytic continuation by means of the methods of divergent series
Application of a Tauberian theorem to finite model theory.
Approximation by Abel means and Tauberian Theorems in sequences spaces
Approximation on the semi-infinite interval.
Axiomatic theory of divergent series and cohomological equations
A general theory of summation of divergent series based on the Hardy-Kolmogorov axioms is developed. A class of functional series is investigated by means of ergodic theory. The results are formulated in terms of solvability of some cohomological equations, all solutions to which are nonmeasurable. In particular, this realizes a construction of a nonmeasurable function as first conjectured by Kolmogorov.
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 variation sequences of order k and the representation of null sequences.
Boundness of Cesàro means operators.
Cesàro statistical core of complex number sequences.
Cesàro summability factors and a comparison of convergence rates
Characterization for relations on some summability methods.
Charakterisierungen für Hausdorff-Matrizen.
Convergence and Summability of Gabor Expansions at the Nyquist Density.
Correction to "A Generalization of Tauber's Theorem and Some Tauberian Constants (IV)".
Corrigendum: On summability of Fourier series.
Criteria for membership of the Besov spaces BS pq.