On the strong Cesàro summability of double orthogonal series
On the strong lacunary convergence and strong Cesàro summability of sequences of real-valued functions.
On the weight matrices of linear difference equations
On two summability methods
Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences
Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and , then . The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof of Vijayaraghavan’s...
Permutations preserving Cesàro mean, densities of natural numbers and uniform distribution of sequences
We are interested in permutations preserving certain distribution properties of sequences. In particular we consider -uniformly distributed sequences on a compact metric space , 0-1 sequences with densities, and Cesàro summable bounded sequences. It is shown that the maximal subgroups, respectively subsemigroups, of leaving any of the above spaces invariant coincide. A subgroup of these permutation groups, which can be determined explicitly, is the Lévy group . We show that is big in the...
Product Theorems for Certain Summability Methods in Non-archimedean Fields
In this paper, denotes a complete, non-trivially valued, non-archimedean field. Sequences and infinite matrices have entries in The main purpose of this paper is to prove some product theorems involving the methods and in such fields
Repeated convergence and fractional differences
Section of Euler summability method.
Sobre c-dualidad y espacios c-perfectos.
Sobre sumabilidad Cesáro en el espacio CS (I).
Some absolutely effective product methods.
Some analogues of Knopp's core theorem.
Some inclusion theorems for absolute summability
Some properties of Riesz means and spectral expansions. (With an appendix by R. A. Gustafson).
Some remarks on strong approximation by Cesàro means
Some Tauberian theorems for Euler and Borel summability.
Spectral decompositions, ergodic averages, and the Hilbert transform
Let U be a trigonometrically well-bounded operator on a Banach space , and denote by the sequence of (C,2) weighted discrete ergodic averages of U, that is, . We show that this sequence of weighted ergodic averages converges in the strong operator topology to an idempotent operator whose range is x ∈ : Ux = x, and whose null space is the closure of (I - U). This result expands the scope of the traditional Ergodic Theorem, and thereby serves as a link between Banach space spectral theory and...
Spectral Riesz-Cesàro means: How the square root function helps us to see around the world.
Statistical convergence of Walsh-Fourier series.