Biorthogonal series generated by dihedral group. (Q1599424)

Let a domain \(D_0\subset D_1\), where \(D_1\) is the domain bounded by the arcs \(| z\pm \sqrt{2}i/2|= \sqrt{2}/2\). In the paper the author studies for analytic functions approximate properties of -- the system of rational functions \(g_n(z)= h_n(-z)- h_n(z)\), \(n\in\mathbb{N}\), where \(h_n(z)= i(iz- \sqrt{2}/2)^{-n-1}\); -- the system of Cauchy integrals \(f_n(z)= \int_{\partial D_0} b_n(t)(z- t)^{-1} dt\); \(z\not\in D_0\), \(n\in\mathbb{N}_0\), where \(b_n(t)= (a(t)- \sqrt{2}/2)^n\); -- the system of entire functions of exponential type \(F_n(z)= \int_{\partial D_0} b_n(t) \exp(zt)\,dt\), \(n\in\mathbb{N}\), where \(a(t):\partial D\to \partial D\) is a homeomorphism, \(D\) is a circular sector, \(D_0\subset D\).