The square-root-oscillation conjecture for radial Toeplitz operators

Let $n$ be the fixed positive integer defining the polyanalytic Bargmann–Segal–Fock setting. A bounded square-root-oscillating sequence is a bounded sequence with the square-root oscillation property used to describe the corresponding sequence C*-algebra. Square-root-oscillation conjecture. The C*-algebra $\mathcal{T}_{(n)}(\operatorname{RB})$ is isometrically isomorphic to the C*-algebra of bounded square-root-oscillating sequences. The concept is known in the ordinary analytic case $n=1$, but the asserted description for general $n$ is the conjectural extension in this setting.