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Dense linear manifolds of monsters
(Elsevier, 2002-12)
In this paper the new concept of totally omnipresent operators is introduced. These operators act on the space of holomorphic functions of a domain in the complex plane. The concept is more restrictive than that of ...
Artículo
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A spectral radius type formula for approximation numbers of composition operators
(Elsevier, 2014-12-15)
For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞[an(Cφ)]1/n=e−1 ...
Artículo
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Nevanlinna counting function and Carleson function of analytic maps
(Springer, 2011-10)
We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.
Artículo
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Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions
(Elsevier, 2021)
We compare the rate of decay of singular numbers of a given composition operator acting on various Hilbert spaces of analytic functions on the unit disk D. We show that for the Hardy and Bergman spaces, our results are ...
Artículo
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U-operators
(Cambridge University Press, 2005-02)
Inspired by a statement of W. Luh asserting the existence of entire functions having together with all their derivatives and antiderivatives some kind of additive universality or multiplicative universality on certain ...
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Some new properties of composition operators associated with lens maps
(Springer, 2013-05)
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H2. The last ones are connected with ...
Artículo
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Extended eigenvalues of composition operators
(Elsevier, 2021-12-15)
A complex scalar λ is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX=λXA. The results in this paper provide a full solution to the ...
Artículo
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Subspaces of frequently hypercyclic functions for sequences of composition operators.
(Springer, 2019-02)
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such a criterion improves some already known ...
Artículo
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Compact composition operators on the Dirichlet space and capacity of sets of contact points
(Elsevier, 2013-02-15)
We prove several results about composition operators on the Dirichlet space D⁎. For every compact set K⊆∂D of logarithmic capacity , there exists a Schur function φ both in the disk algebra A(D) and in D⁎ such that the ...
Artículo
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Some revisited results about composition operators on Hardy spaces
(European Mathematical Society, 2012)
We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on ...