2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71755Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related H-infinity optimization problem. The theorems here remove a number of unnatural assumptions required in an earlier work by the same author, "Polynomial hulls and H-infinity control for a hypoconvex constraint." (See http://www.arxiv.org/abs/math.CV/0001039)12 pages. To appear in the Journal of Geometric Analysis. This work is the sequel to another paper by the same author, (see http://www.arxiv.org/abs/math.CV/0001039) "Polynomial hulls and H-infinity control for a hypoconvex constraint."Complex VariablesOptimization and Control32E30, 49K35 (Primary) 30E25 (Secondary)text