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Abstract: We use Salem’s method [ 13 , 14 ] to prove an inequality of Kwapie´n and Pełczy´nski concerning a lower bound for partial sums of series of bi-orthogonal vectors in a
To study the arithmetic of the formal modules in an arbitrary local field and to derive explicit formulas for the generalized Hilbert pairing on these modules we should
In [6] the second author discovered a general scheme, with the help of nonstandard analysis, how one can derive a theorem about the upper Banach density parallel to each
But the Malliavin calculus for Gaussian processes can be adapted to it, Skorohod stochastic integrals can be defined, and it will allow us to derive an Itˆ o formula when the
We show that Varadhan’s small time asymptotics for densities of the solution of a stochastic differ- ential equation in R n [8] carries over to a Hilbert space-valued
We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space E which is continuously and densely embedded in a
Einmahl and Mason [ 3 ] looked at a large class of kernel type estimators including density and regression function estimators and determined the precise order of uniform convergence
We now consider the following example of probabilistic ϕ-2-normed space having as base spaces sets of random variables with values in a Banach algebra.. The study of
