Results 1  10
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20
R.“Seventy years of Rajchman measures
 J. Fourier Anal. Appl. Kahane special issue
, 1995
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FREQUENTLY HYPERCYCLIC OPERATORS
"... Abstract. We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators T on separable complex Fspaces: T is frequently hypercyclic if there exists a vector x such that for every nonempty open subset U of X, thesetofintegersnsuch that T nx bel ..."
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Cited by 6 (3 self)
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Abstract. We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators T on separable complex Fspaces: T is frequently hypercyclic if there exists a vector x such that for every nonempty open subset U of X, thesetofintegersnsuch that T nx belongs to U has positive lower density. We give several criteria for frequent hypercyclicity, and this leads us in particular to study linear transformations from the point of view of ergodic theory. Several other topics which are classical in hypercyclicity theory are also investigated in the frequent hypercyclicity setting. 1.
Convexity Ranks in Higher Dimension
 Fundamenta Mathematicae
, 2000
"... A subset of a vector space is called countably convex if it is a countable union of convex sets. Classication of countably convex subsets of topological vector spaces is addressed in this paper. ..."
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Cited by 2 (1 self)
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A subset of a vector space is called countably convex if it is a countable union of convex sets. Classication of countably convex subsets of topological vector spaces is addressed in this paper.
ANALYTIC REPRESENTATION OF FUNCTIONS AND A NEW TYPE OF QUASIANALYTICITY
, 2004
"... ABSTRACT. We characterize precisely the possible rate of decay of the antianalytic half of a trigonometric series converging to zero almost everywhere. 1. ..."
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Cited by 1 (1 self)
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ABSTRACT. We characterize precisely the possible rate of decay of the antianalytic half of a trigonometric series converging to zero almost everywhere. 1.
MAXIMAL SMOOTHNESS OF THE ANTIANALYTIC PART OF A TRIGONOMETRIC NULL SERIES
, 2005
"... ABSTRACT. We proved recently [6] that the antianalytic part of a trigonometric series,converging to zero almost everywhere, may belong to L 2 on the circle. Here we prove that it can even be C ∞ , and we characterize precisely the possible degree of smoothness in terms of the rate of decrease of th ..."
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ABSTRACT. We proved recently [6] that the antianalytic part of a trigonometric series,converging to zero almost everywhere, may belong to L 2 on the circle. Here we prove that it can even be C ∞ , and we characterize precisely the possible degree of smoothness in terms of the rate of decrease of the Fourier coefficients. This sharp condition might be viewed as a “new quasianalyticity ”.
A NULL SERIES WITH SMALL ANTIANALYTIC PART.
, 2005
"... ABSTRACT. We show that it is possible for an L 2 function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to not belong to the Hardy space H 2. A consequence in the uniqueness theory is obtained. ..."
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ABSTRACT. We show that it is possible for an L 2 function on the circle, which is a sum of an almost everywhere convergent series of exponentials with positive frequencies, to not belong to the Hardy space H 2. A consequence in the uniqueness theory is obtained.
The σideal generated by Hsets
, 2011
"... It is consistent with the axioms of set theory that the circle T can be covered by ℵ1 many closed sets of uniqueness while a much larger number of Hsets is necessary to cover it. In the proof of this theorem, the descriptive set theoretic phenomenon of overspill appears, and it is reformulated as a ..."
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It is consistent with the axioms of set theory that the circle T can be covered by ℵ1 many closed sets of uniqueness while a much larger number of Hsets is necessary to cover it. In the proof of this theorem, the descriptive set theoretic phenomenon of overspill appears, and it is reformulated as a natural forcing preservation principle that persists through the operation of countable support product.
Overspill and forcing
, 2011
"... The overspill phenomenon in descriptive set theory corresponds to a forcing preservation property, with a fusion type infinite game associated to it. As an application, it is consistent with the axioms of set theory that the circle T can be covered by ℵ1 many closed sets of uniqueness while a much l ..."
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The overspill phenomenon in descriptive set theory corresponds to a forcing preservation property, with a fusion type infinite game associated to it. As an application, it is consistent with the axioms of set theory that the circle T can be covered by ℵ1 many closed sets of uniqueness while a much larger number of Hsets is necessary to cover it.