Inverspositive Operatoren und Taubersätze in der Erneuerungstheorie.
Le théorème taubérien de Wiener et l'équation de la chaleur
Marcinkiewicz multipliers of higher variation and summability of operator-valued Fourier series
Let , where, for 1 ≤ r < ∞, (resp., ) denotes the class of functions (resp., bounded functions) g: → ℂ such that g has bounded r-variation (resp., uniformly bounded r-variations) on (resp., on the dyadic arcs of ). In the author’s recent article [New York J. Math. 17 (2011)] it was shown that if is a super-reflexive space, and E(·): ℝ → () is the spectral decomposition of a trigonometrically well-bounded operator U ∈ (), then over a suitable non-void open interval of r-values, the condition...
Measuring asymptotic convexity
Mercerian and Tauberian Theorems for Differences.
Necessary and sufficient conditions under which convergence follows from summability by weighted means.
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function s is slowly...
Negative Resultate über Tauber-Bedingungen.
On a Tauberian theorem for Euler summability.
On a theorem of W. Meyer-König and H. Tietz.
On Conjugate pi-variation and the Coefficients of Power Series
On Multidimensional Generalizations Of Regularly Varying Functions And Tauberian And Abelian Theorems
On Tauberian constants for the summability
On the Laplace Transforms of Logconcave Densities
On the Tauberian constant in the Ikehara theorem
On the value of a distribution at a point
On Valiron and Circle Convergence.
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...
O-Regularly Varying Convergence Moduli of Fourier and Fourier-Stieltjes Series.
Permanenz- und Taubersätze bei pV-Summierung.