On the Phragmén-Lindelöf principle for entire power series on a Banach algebra - Contreras-Juárez, Roberto; Palomino-Jiménez, Carlos (Communications in Mathematics and Applications, 2015)
Many authors have managed to successfully extend the classical theory  of analytic functions to functions deï¬ned on more abstract spaces (see for example [3, 8, 9]). The purpose of this paper is to provide a bit in this direction. In this paper an extension of the Phragmén-Lindelöf principles of the classical theory to the functions expressed as power series on a Banach algebra not necessarily commutative, of course, involving concepts such as harmonic and subharmonic, is introduced.