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Commutator of composition operators with adjoints of composition operators

Complex Variables and Elliptic Equations, 2012
We characterize the compactness of the linear fractionally induced commutator in terms of the function theoretic properties of ϕ and ψ. We show that in the automorphic case the commutator is compact if and only if ϕ and ψ are simple rotations of the unit disc.
John H. Clifford   +2 more
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Compositions of Set Operations

Canadian Journal of Mathematics, 1970
The set operations under consideration are Borel operations and Souslin's operation (). With respect to a given family of sets and in a setting free of any topological structure there are defined three Borel families (Definitions 3.1) and the family of Souslin sets (Definition 4.1).
Bressler, D. W., Cayford, A. H.
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A model for composable composition operators

Proceedings of the 9th International Conference on Aspect-Oriented Software Development, 2010
A considerable amount of research, especially within the OO and AOSD communities, has focused on understanding the potential and limitations of various composition techniques. This has led to a large amount of proposals for alternative composition techniques, including many variations of message dispatch, inheritance, and aspect mechanisms.
Havinga, Wilke   +2 more
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Composition operators on potential spaces

Proceedings of the American Mathematical Society, 1992
By a result of B. Dahlberg, the composition operators T H
Adams, David R., Frazier, Michael
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Essential Norms of Composition Operators

Integral Equations and Operator Theory, 2004
Recently, there has been considerable interest in studying lower and upper estimates for the essential norms of composition operators in function spaces. Sometimes, as a consequence, a necessary and sufficient condition for the composition operator to be compact on the function space can be obtained.
Gorkin, Pamela, MacCluer, Barbara D.
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Operator regularization and composite operators

Canadian Journal of Physics, 1990
We demonstrate how operator regularization can be used to compute radiative corrections to Green's functions involving composite operators. No divergences are encountered and no symmetry-breaking regulating parameter need be introduced into the initial Lagrangian.
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UNIFORMLY BOUNDED COMPOSITION OPERATORS

Bulletin of the Australian Mathematical Society, 2015
We prove that if a uniformly bounded (or equidistantly uniformly bounded) Nemytskij operator maps the space of functions of bounded ${\it\varphi}$-variation with weight function in the sense of Riesz into another space of that type (with the same weight function) and its generator is continuous with respect to the second variable, then this generator ...
Głazowska, Dorota, Matkowski, Janusz
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Implementations of program composition operations

1994
This paper reports on a number of implementations for a suite of composition operations of logic programs. We present and compare three implementations, which rely on different techniques: metaprogramming, program transformations, and extensions to the WAM, respectively.
Brogi A   +7 more
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The Norms of Compositions of Arithmetic Operators

Bulletin of the London Mathematical Society, 1987
Weighted inequalities which widely generalize the Turán-Kubilius inequality are established. The following is typical: Let w(m) be a non- negative real-valued arithmetic function which satisfies w(q) \(\ll 1\), w(qm) \(\ll w(q)w(m)\) uniformly for prime-powers q and positive integers m, \((q,m)=1\).
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Operational and compositional semantics of synchronous automaton compositions

2006
The state/transition paradigm has been used extensively for the description of event-driven, parallel systems. However, the lack for hierarchic structure in such descriptions usually prevents us from using this paradigm in a real programming language. We propose the Argos language for reactive systems. The basic components of a program are input/output-
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