and $\mu$ — probability measure on $S$, given by the formula $$\mu(\d x,\d y)=\frac{1}{2\pi^2}\sqrt{27-18z\z+4z^3+4\z^3-\z^2z^2}dxdy;\quad (z=x+iy).$$ The normalization constant in this formula was calculated in [@N47] (see also [@N45; @N24]).

![Steiner hypocycloid ](HS-param_2){width="6.0cm"}

Chebyshev — Koornwinder oscillator (ChK-oscillator)
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In the work [@N46] we applied the construction [@N16] of the generalized oscillator connected with a system of orthogonal polynomials on the real axis to the case of ChK-polynomials of two variables. Chebyshev — Koornwinder oscillator (ChK-oscillator) was considered in [@N46] as a union of three oscillators: sectorial, radial, and boundary ones. To describe them it is convenient to use the following decompositions of the space $\H$ (which we consider as the Fock space), in the direct sums of subspaces: $$\label{13-1.2}
\H=\bigoplus_{N=0}^{\infty}\H^{(N)},\quad \H=\He\bigoplus\Ho,$$ where $N$-particle sector $\H^{(N)}$ is the closure in $\H$ of the linear span of set of basis vectors $\left\{U_{k,\,l}(z,\overline{z})\left|\right.k+l=N\right\}$, and subspaces $\He$ è $\Ho$ are the closures of linear spans of the following sets $$\left\{U_{k,\,l}(z,\overline{z})\left|\right.k+l=2n\right\}_{n=0}^{\infty}
\quad \text{and} \quad
\left\{U_{k,\,l}(z,\overline{z})\left|\right.k+l=2n+1\right\}_{n=0}^{\infty},$$ respectively. Moreover, we use the following subspaces $\Hco$ and $\Hoc$ which are the closures of linear spans of the sets $$\left\{U_{k,\,0}(z,\overline{z})\right\}_{k=0}^{\infty}
\quad \text{and} \quad
\left\{U_{0,\,l}(z,\overline{z})\right\}_{l=0}^{\infty},$$ and the spaces $\mathcal{H}^{\bullet,\,0}$ and $\mathcal{H}^{0,\,\bullet}$ defined by $$\mathcal{H}^{\bullet,\,0}=\H\ominus\Hco,\qquad \mathcal{H}^{0,\,\bullet}=\H\ominus\Hoc.$$ As in the case of 