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Composition and Decomposition of Positive Linear Operators (VIII)
Axioms, 2023 In a series of papers, most of them authored or co-authored by H. Gonska, several authors investigated problems concerning the composition and decomposition of positive linear operators defined on spaces of functions. For example, given two operators with known properties, A and B, we can find the properties of the composed operator A∘B, such as the ...
Ana Maria Acu, Ioan Rasa, Andra Seserman
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Disjoint hypercyclic linear fractional composition operators
Journal of Mathematical Analysis and Applications, 2011 The first and the third authors are supported in part by MICINN and FEDER, Projects MTM2007-64222 and MTM2010-14909. The third author is also supported by Generalitat Valenciana, Project PROMETEO/2008/101. We thank the referees for their comments and suggestions.
Bes, J. +2 more
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Linear Combinations of Composition Operators on the Bloch Spaces [PDF]
Canadian Journal of Mathematics, 2011 Abstract We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.
Takuya Hosokawa +2 more
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Norms of linear-fractional composition operators [PDF]
Transactions of the American Mathematical Society, 2003 Summary: We obtain a representation for the norm of the composition operator \(C_\phi\) on the Hardy space \(H^2\) whenever \(\phi\) is a linear-fractional mapping of the form \(\phi(z) = b/(cz +d)\). The representation shows that, for such mappings \(\phi\), the norm of \(C_\phi\) always exceeds the essential norm of \(C_\phi\).
Bourdon, Paul S. +3 more
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On the composition and decomposition of positive linear operators (VII)
Applicable Analysis and Discrete Mathematics, 2021 In the present paper we study the compositions of the piecewise linear interpolation operator S?n and the Beta-type operator B?n, namely An:= S?n ?B?n and Gn := B?n ? S?n. Voronovskaya type theorems for the operators An and Gn are proved, substantially improving some corresponding known results.
Acu, Ana Maria, Raşa, Ioan
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Linear and Logarithmic Time Compositions of Quantum Many-Body Operators [PDF]
Physical Review Letters, 2017 We develop a generalized framework for constructing many-body-interaction operations either in linear time, or in logarithmic time with a linear number of ancilla qubits. Exact gate decompositions are given in particular for Pauli strings, many-control Toffoli gates, number-~and parity-conserving interactions, Unitary Coupled Cluster operations, and ...
Motzoi, F. +2 more
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Linear relations in the Calkin algebra for composition operators [PDF]
Transactions of the American Mathematical Society, 2007 We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?
Kriete, Thomas, Moorhouse, Jennifer
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Components of linear-fractional composition operators
Journal of Mathematical Analysis and Applications, 2003 Let \(\phi\) denote a holomorphic function on the open unit disc \(U\) in the complex plane with \(\phi(U) \subset U\). The composition operator \(C_{\phi}(f):=f \circ \phi\) is bounded in the Hardy space \(H^2\). Denote by \(\text{comp} (H^2)\) the collection of all composition operators on \(H^2\) endowed with the metric induced by the operator norm.
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Renormalizability of the local composite operator Aμ2 in linear covariant gauges [PDF]
Physics Letters B, 2003 The local composite operator $A_μ^{2}$ is analysed within the algebraic renormalization in Yang-Mills theories in linear covariant gauges. We establish that it is multiplicatively renormalizable to all orders of perturbation theory. Its anomalous dimension is computed to two-loops in the MSbar scheme.
Dudal, David +6 more
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ITERATED COMPOSITIONS OF LINEAR OPERATIONS ON SETS OF POSITIVE UPPER DENSITY [PDF]
International Journal of Number Theory, 2009 Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density.
Hegyvári, Norbert +2 more
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