Noncommutative partially convex rational functions

• Michael Jury ^[1] ; Igor Klep ^[2] ; Mark E. Mancuso ^[3] ; Scott McCullough ^[1] ; James Eldred Pascoe ^[1]
  1. [1] University of Florida

     University of Florida

     Estados Unidos

     
  2. [2] University of Ljubljana

     University of Ljubljana

     Eslovenia

     
  3. [3] Lafayette College

     Lafayette College

     City of Easton, Estados Unidos

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 3, 2022, págs. 731-759
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially convex admit novel butterfly-type realizations that necessitate square roots. A strengthening of partial convexity arising in connection with BMIs – xy-convexity – is also considered. A characterization of xy-convex polynomials is given.