Spaces on which every pointwise convergent series of continuous functions converges pseudo-normally

Spaces on Which Every Pointwise Convergent Series of Continuous Functions Converges Pseudo-normally

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

Pointwise Multipliers of Besov Spaces of Smoothness Zero and Spaces of Continuous Functions

A continuous-time observer which converges in finite time

the control law (3) does not only improves the transient performance, but also provides smoother outputs. It is important to stress that a better performance can still be achieved with (28) and (30). However, as discussed in Remark IV.1, increasing gains would not only cause more peaks in the outputs, but it might also yield saturation, especially for 2. V. CONCLUSION The tracking control probl...

Pointwise multiplication operators on weighted Banach spaces of analytic functions

For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator Mφ, Mφ(f)=φf , on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Therefore we characterize when Mφ is Fredholm or is an isomorphism into. We study also cyclic phenomena of the adjoint map M ′ φ.

A nowhere convergent series of functions converging somewhere after every non-trivial change of signs

We construct a sequence of continuous functions (hn) on any given uncountable Polish space, such that ∑ hn is divergent everywhere, but for any sign sequence (εn) ∈ {−1,+1} N which contains infinitely many −1 and +1 the series ∑ εnhn is convergent at at least one point. We can even have hn → 0, and if we take our given Polish space to be any uncountable closed subset of R, we can require that e...