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12 results on '"R. Trautner"'

5. RATIO TAUBERIAN THEOREMS FOR LAPLACE TRANSFORMS WITHOUT MONOTONICITY ASSUMPTIONS

Author

R Trautner and Ulrich Stadtmüller

Subjects
Post's inversion formula, Laplace transform, Laplace principle, General Mathematics, Laplace transform applied to differential equations, Mathematical analysis, Two-sided Laplace transform, Inverse Laplace transform, Monotonic function, Mathematics, Abelian and tauberian theorems
Published
1985

7. An Inclusion Relation for Abel, Borel, and Lambert Summability

Author

Wolfgang Gawronski, R. Trautner, and H. Siebert

Subjects
Pure mathematics, Borel's lemma, General Mathematics, Calculus, Inclusion relation, Mathematics
Abstract

In this paper a new type of inclusion theorem concerning Abel, Borel and Lambert summability is established. To state our results we need some definitions and notations. With a formal series ∑k=0∞ak, ak∈ C, and its partial sums snwe associate the seriesThen ∑k=0∞ ak is said to be summable to the value s(a) by Abel's method, if (1.1) is convergent for |v| > 1 and limv→1+A(v)= s,(b) by Lambert's method, if (1.2) is convergent for |v| > 1 and limv→1+L(v)= s,(c) by Borel's method, if (1.3) is convergent for all x ∈ R and limx→+∞B(x)= s

Published
1980

9. ASYMPTOTIC BEHAVIOUR OF DISCRETE LINEAR PROCESSES

Author

R. Trautner and U. Stadtmüller

Subjects
Statistics and Probability, Discrete mathematics, Probability space, Law of large numbers, Applied Mathematics, Linear process, Order (group theory), Limit (mathematics), Statistics, Probability and Uncertainty, Central limit theorem, Mathematics
Abstract

We consider the linear process Yn(ω) =ΣAk(ω) ·Xn-k (ω) on a probability space (Ω, P) and ask for sufficient conditions in order to get a limit theorem for (Yk) if the corresponding limit theorem for (Xk) is true.

Published
1985

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