Symbols of some operator sequences and quadrature methods for solving singular integral equations with conjugation (Q1320678)

The authors give necessary and sufficient conditions for stability of sequences of the form \[ A_ n= \widetilde a_ n \alpha_ n + \widetilde b_ n\cdot \beta_ n+ (\widetilde c_ n\cdot \gamma_ n+ \widetilde d_ n\cdot \Theta_ n) M+ R_ n\qquad n= 1,2,\dots \] where \(a,b,c,d,\alpha,\beta,\gamma,\Theta\in P\subset (T)\), \(\| R_ n\|\to 0\) as \(n\to \infty\), and \[ M\xi^{(n)}= M(\xi^{(n)}_ 0, \xi^{(n)}_ 1,\dots, \xi^{(n)}_{n- L})= (\overline{\xi^{(n)}_ 0}, \overline{\xi^{(n)}_ 0},\dots,\overline{\xi^{(n)}_{n- L}}). \] These conditions are used to study the convergence of some quadrature methods for solving singular integral equations with conjugation on smooth curves.