Darren C. Ong

activity

20112026

most citedAlmost Everything About the Unitary Almost Mathieu Operator

14 citations · 77 across the 20 of their papers we have counts for

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Showing 2020Show all

4 papers · 1 filter

math.SP2020

On Simon's Hausdorff Dimension Conjecture

David Damanik, Jake Fillman, Shuzheng Guo +1

Barry Simon conjectured in 2005 that the Szegő matrices, associated with Verblunsky coefficients ${α_{n}}_{n \in Z_{+}}$ obeying $\sum_{n = 0}^{\infty} n^{γ} ∣ α_{n} ∣^{2} < \infty$ for…

math.SP2020

Simon's OPUC Hausdorff Dimension Conjecture

David Damanik, Shuzheng Guo, Darren C. Ong

We show that the Szegő matrices, associated with Verblunsky coefficients ${α_{n}}_{n \in Z_{+}}$ obeying $\sum_{n = 0}^{\infty} n^{γ} ∣ α_{n} ∣^{2} < \infty$ for some $γ \in (0, 1)$ , are b…

math.HO2020★ 4 cited

Quasiperiodic Music

Darren C. Ong

Using the definition of quasiperiodic function as a motivation, we introduce the idea of quasiperiodic music and detail the composition process of a quasiperiodic music piece, Rain…

math.SP2020★ 3 cited

Subordinacy Theory for Extended CMV Matrices

Shuzheng Guo, David Damanik, Darren C. Ong

We develop subordinacy theory for extended CMV matrices. That is, we provide explicit supports for the singular and absolutely continuous parts of the canonical spectral measure as…