Arguments of zero sets in the Dirichlet space

2010 ◽  
pp. 143-148 ◽  
Author(s):  
Javad Mashreghi ◽  
Thomas Ransford ◽  
Mahmood Shabankhah
Keyword(s):  
Dirichlet Space ◽  
Zero Sets

Zero sets and uniqueness sets with one cluster point for the Dirichlet space

2009 ◽  
Vol 357 (2) ◽  
pp. 498-503 ◽  
Author(s):  
Javad Mashreghi ◽  
Mahmood Shabankhah
Keyword(s):  
Dirichlet Space ◽  
Cluster Point ◽  
Zero Sets ◽  
Uniqueness Sets

scholarly journals On Zero Sets in the Dirichlet Space

2011 ◽  
Vol 22 (4) ◽  
pp. 1055-1070 ◽  
Author(s):  
Karim Kellay ◽  
Javad Mashreghi
Keyword(s):  
Dirichlet Space ◽  
Zero Sets

Semigroups of Composition Operators on the Dirichlet Space

1996 ◽  
Vol 30 (1-2) ◽  
pp. 165-173 ◽  
Author(s):  
Aristomenis G. Siskakis
Keyword(s):  
Composition Operators ◽  
Dirichlet Space

Powers of the ideal of Lebesgue measure zero sets

1991 ◽  
Vol 56 (1) ◽  
pp. 103-107
Author(s):  
Maxim R. Burke
Keyword(s):  
Partial Order ◽  
Lebesgue Measure ◽  
Regular Cardinal ◽  
Measure Zero ◽  
Lebesgue Measure Zero ◽  
Zero Sets ◽  
Covering Lemma ◽  
Inner Model ◽  
The Ideal

AbstractWe investigate the cofinality of the partial order κ of functions from a regular cardinal κ into the ideal of Lebesgue measure zero subsets of R. We show that when add () = κ and the covering lemma holds with respect to an inner model of GCH, then cf (κ) = max{cf(κκ), cf([cf()]κ)}. We also give an example to show that the covering assumption cannot be removed.

scholarly journals Some Hilbert spaces related with the Dirichlet space

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Nicola Arcozzi ◽  
Pavel Mozolyako ◽  
Karl-Mikael Perfekt ◽  
Stefan Richter ◽  
Giulia Sarfatti
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Dirichlet Space

AbstractWe study the reproducing kernel Hilbert space with kernel k

Ultrafilter-completeness on zero-sets of uniformly continuous functions

2019 ◽  
Vol 252 ◽  
pp. 27-41
Author(s):  
Asylbek A. Chekeev ◽  
Tumar J. Kasymova
Keyword(s):  
Continuous Functions ◽  
Zero Sets ◽  
Uniformly Continuous

Extension of S-plurisubharmonic currents across zero sets of plurisubharmonic functions

2018 ◽  
Vol 64 (8) ◽  
pp. 1345-1352
Author(s):  
Ahmad K. Al Abdulaali ◽  
Hassine El Mir
Keyword(s):  
Plurisubharmonic Functions ◽  
Zero Sets

Bergman Spaces on Disconnected Domains

1996 ◽  
Vol 48 (2) ◽  
pp. 225-243
Author(s):  
Alexandru Aleman ◽  
Stefan Richter ◽  
William T. Ross
Keyword(s):  
Measure Zero ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Invariant Subspaces ◽  
Compact Set ◽  
Bounded Region ◽  
Area Measure ◽  
Weak Star ◽  
Harmonic Dirichlet Space ◽  
Disconnected Domains

AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.

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