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Artículo
Operators with dense images everywhere
(Elsevier, 2001-11-01)
In this paper, the authors introduce the dense-image operators T as those with a wild behaviour near of the boundary of a domain G, via certain subsets. The relationship with other kinds of operators with wild behaviour ...
Artículo
Lineability and modes of convergence
(Springer, 2020-01)
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are ...
Artículo
Lacunary non-continuable boundary-regular holomorphic functions with universal properties
(National Academy of Sciences of the Republic of Armenia, 2006)
A holomorphic function in a Jordan domain G in the complex plane is constructed with all its derivatives extending continuously up to the boundary G that happens to be a natural boundary of In addition the action of a ...
Artículo
Compositional hypercyclicity equals supercyclicity
(University of Houston, 2007)
In this note it is proved that the sequence of composition operators generated by automorphisms of a simply connected domain strictly contained in the complex plane is hypercyclic –that is, possesses some dense orbit– ...
Artículo
Strongly omnipresent integral operators
(Springer, 2002-12)
An operator T on the space H(G) of holomorphic functions on a domain G is strongly omnipresent whenever there is a residual set of functions f ∈ H(G) such that T f exhibits an extremely “wild” behaviour near the boundary. ...
Artículo
Real-Analytic Non-Integrable Functions on the Plane with Equal Iterated Integrals
(Springer, 2021-12-16)
In this note, a vector space of real-analytic functions on the plane is explicitly constructed such that all its nonzero functions are non-integrable but yet their two iterated integrals exist as real numbers and coincide. ...
Artículo
Pseudo-Fubini Real-Entire Functions on the Plane
(Springer, 2022-09-09)
In this note, it is proved the existence of a c -dimensional vector space of real-entire functions all of whose nonzero members are non-integrable in the sense of Lebesgue but yet their two iterated integrals exist as ...
Artículo
Anti M-Weierstrass function sequences
(Elsevier, 2020-11-01)
Large algebraic structures are found inside the space of sequences of continuous functions on a compact interval having the property that, the series defined by each sequence converges absolutely and uniformly on the ...
Artículo
Large algebras of singular functions vanishing on prescribed sets
(Springer, 2016-06-21)
In this paper, the non-vacuousness of the family of all nowhere analytic infinitely differentiable functions on the real line vanishing on a prescribed set Z is characterized in terms of Z. In this case, large algebraic ...
Artículo
Universal functions with small derivatives and extremely fast growth
(De Gruyter, 2002-03)