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Full-Text Articles in Physical Sciences and Mathematics
Composition Operators And A Pull-Back Measure Formula, Valentin Matache
Composition Operators And A Pull-Back Measure Formula, Valentin Matache
Mathematics Faculty Publications
A pull-back measure formula obtained in some particular cases by E. A. Nordgren and this author is generalized in the framework of boundary measures for zero-free Nevanlinna class fuctions on the unit polydisk. The formula is used to characterize the zero-free Nevanlinna class functions which are solutions of Schröder's equation induced by a polydisk automorphism ϕ (i.e. to determine the zero-free functionsf belonging to the Nevanlinna class which are solutions of the functional equationf ° π=λf, for some constant λ), thus generalizing earlier results obtained by R. Mortini and this author.
Numerical Ranges Of Composition Operators, Valentin Matache
Numerical Ranges Of Composition Operators, Valentin Matache
Mathematics Faculty Publications
Composition operators on the Hilbert Hardy space of the unit disk are considered. The shape of their numerical range is determined in the case when the symbol of the composition operator is a monomial or an inner function fixing 0. Several results on the numerical range of composition operators of arbitrary symbol are obtained. It is proved that 1 is an extreme boundary point if and only if 0 is a fixed point of the symbol. If 0 is not a fixed point of the symbol 1 is shown to be interior to the numerical range. Some composition operators whose …
Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski
Iteration Of Λ-Complete Forcing Notions Not Collapsing Λ+, Andrzej Roslanowski
Mathematics Faculty Publications
We look for a parallel to the notion of “proper forcing” among λ-complete forcing notions not collapsing λ+. We suggest such a definition and prove that it is preserved by suitable iterations.