Subperiodic trigonometric interpolation and quadrature

We study theoretically and numerically trigonometric interpolation on symmetric subintervals of [-π,π][-π,π], based on a family of Chebyshev-like angular nodes (subperiodic interpolation). Their Lebesgue constant increases logarithmically in the degree, and the associated Fejér-like trigonometric quadrature formula has positive weights. Applications are given to the computation of the equilibrium measure of a complex circle arc, and to algebraic cubature over circular sectors.