Splitting the Riesz basis condition for systems of dilated functions through Dirichlet series

  title={Splitting the Riesz basis condition for systems of dilated functions through Dirichlet series},
  author={Jorge Antezana and Daniel Carando and Melisa Scotti},
  journal={Journal of Mathematical Analysis and Applications},
1 Citations
Multipliers for Hardy spaces of Dirichlet series
We characterize the space of multipliers from the Hardy space of Dirichlet series H 𝑝 into H 𝑞 for every 1 ≤ 𝑝, 𝑞 ≤ ∞ . For a fixed Dirichlet series, we also investigate some structural properties


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The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk
  • Hui Dan, K. Guo
  • Mathematics
    Journal of the London Mathematical Society
  • 2020
The classical completeness problem raised by Beurling and independently by Wintner asks for which ψ∈L2(0,1) , the dilation system {ψ(kx):k=1,2,…} is complete in L2(0,1) , where ψ is identified with
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— Completeness of a dilation system (φ(nx))n>1 on the standard Lebesgue space L2(0, 1) is considered for 2-periodic functions φ. We show that the problem is equivalent to an open question on cyclic
Spaces of Dirichlet Series
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As we have seen, a frame {f k } k=1 ∞ in a Hilbert space H has one of the main properties of a basis: given f ∈ H, there exist coefficients {c k } k=1 ∞ ∈ l 2(ℕ) such that f = ∑ k=1 ∞ c k f k . This
A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$
For a function $\varphi$ in $L^2(0,1)$, extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates $\varphi(nx)$, $n=1,2,3,\ldots$, constitutes a
Fourier Analysis on Groups
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact