Abstract. In this work, the relation between input-to-state stability and integral input-to-5 state stability is studied for linear infinite-dimensional systems with an unbounded control operator. 6Although a special focus is laid on the case L ∞ , general function spaces are considered for the inputs. 7We show that integral input-to-state stability can be characterized in terms of input-to-state stability 8 with respect to Orlicz spaces. Since we consider linear systems, the results can also be formulated 9 in terms of admissibility. For parabolic diagonal systems with scalar inputs, both stability notions 10 with respect to L ∞ are equivalent. 11Key words. Input-to-state stability, integral input-to-state stability, C 0 -semigroup, admissibil-12 ity, Orlicz spaces 13 AMS subject classifications. 93D20, 93C05, 93C20, 37C75 14

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A case of Creutzfeldt-Jakob disease (CJD) is reported in a 28-year-old woman who had received a cadaveric dural graft 19 months earlier after resection of a cholesteatoma. The circumstances of the case point to the graft as the most likely source of the disease. Cadaveric dura should be added to the list of materials that may transmit CJD, and it must be very carefully screened if it is used at all for grafting. Autologous tissue should be considered whenever possible.

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This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure or a measure supported on a strip, and complete necessary and sufficient conditions for a bounded embedding are given in many cases.