Self-concordant barriers for cones generated by Chebyshev systems

We explicitly calculate characteristic functions of cones of generalized polynomials corresponding to Chebyshev systems on intervals of the real line and the circle. Thus, in principle, we calculate homogeneous self-concordant barriers for this class of cones. This class includes almost all cones of squares considered in [Y. Nesterov, High Performance Optimization, Kluwer, Dordrecht, 2000, pp. 441-466]. Our construction, however, is applicable to a much broader class of cones.