Abstract. Given a symbol ϕ, i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator C ϕ (f ) = f • ϕ defined on the Banach spaces of holomorphic functions A(D) and H ∞ (D). We obtain different conditions on the symbol ϕ which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behaviour of the iterates of the symbol. As an appendix, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.

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Abstract. We characterize the almost periodic ultradistributions of Beurling and of Roumieu type in terms of classical Bohr almost periodicity. Then we study the Fourier series associated with such an ultradistribution.

Radiofrequency (RF)-based monopolar (MM) and bipolar mode (BM) applicators are used to thermally create coagulation zones (CZs) in biological tissues with the aim of destroying surface tumors and minimizing blood losses in surgical resection. Both modes have disadvantages as regards safely and in obtaining a sufficiently deep coagulation zone (CZ). In this study, we compared both modes versus a switching monopolar mode (SMM) in which the role of the active electrode changes intermittently between the two electrodes of the applicator. In terms of clinical impact, the three modes can easily be selected by the surgeon according to the surgical maneuver. We used computational and experimental models to study the feasibility of working in MM, BM, and SMM and to compare their CZ characteristics. We focused exclusively on BM and SMM, since MM only creates small coagulation zones in the area between the electrodes. The results showed that SMM produces the deepest CZ between both electrodes (33% more than BM) and SMM did not stop the generator when an electrode lost contact with the tissue, as occurred in BM. Our findings suggest that the selective use of SMM and BM with a bipolar applicator offers greater advantages than using each type alone.

We represent every bounded ultradistribution of Beurling or of Roumieu type on R as the boundary value of a holomorphic function. In particular, each almost periodic ultradistribution admits such a representation and we characterize the almost periodic ultradistributions that are boundary values of holomorphic functions in the upper (or lower) half-plane in terms of their spectra.