@inbook{484e7c9a-abd5-4335-a7a6-4f2a392457da,
  abstract     = {{<p>Let H<sub>d</sub><sup>2</sup> be the Drury–Arveson space, and let f∈H<sub>d</sub><sup>2</sup> have bounded argument and no zeros in B<sub>d</sub>. We show that f is cyclic in H<sub>d</sub><sup>2</sup> if and only if logf belongs to the Pick-Smirnov class N<sup>+</sup>(H<sub>d</sub><sup>2</sup>). Furthermore, for non-vanishing functions f∈H<sub>d</sub><sup>2</sup> with bounded argument and H<sup>∞</sup>-norm less than 1, cyclicity can also be tested via iterated logarithms. For example, we show that f is cyclic if and only if log(1+log(1∕f))∈N<sup>+</sup>(H<sub>d</sub><sup>2</sup>). Thus, a sufficient condition for cyclicity is that log(1+log(1∕f))∈H<sub>d</sub><sup>2</sup>. More generally, our results hold for all radially weighted Besov spaces that also are complete Pick spaces.</p>}},
  author       = {{Aleman, Alexandru and Perfekt, Karl Mikael and Richter, Stefan and Sundberg, Carl and Sunkes, James}},
  booktitle    = {{New Trends in Complex Analysis, Fourier Analysis, and Operator Theory}},
  issn         = {{2281-5198}},
  keywords     = {{47A16; Secondary 30H25; Cyclic vectors; Drury-Arveson space; Primary 47B32}},
  language     = {{eng}},
  pages        = {{37--53}},
  publisher    = {{Springer-Verlag Italia s.r.l.}},
  series       = {{Springer INdAM Series}},
  title        = {{Cyclicity and Iterated Logarithms in the Drury–Arveson Space}},
  url          = {{http://dx.doi.org/10.1007/978-981-95-5280-1_2}},
  doi          = {{10.1007/978-981-95-5280-1_2}},
  volume       = {{66}},
  year         = {{2026}},
}