Homage \`{a} A. M. Gleason et I. J. Schark
Steven G. Krantz

TL;DR
This paper investigates the maximal ideal space of the algebra of bounded holomorphic functions on the unit ball in complex n-space, analyzing its structure through Gleason parts, fibers, and boundary concepts using advanced function theory.
Contribution
It extends the analysis of the maximal ideal space of $H^ abla(B)$ by incorporating inner functions and boundary structures, building on prior foundational work.
Findings
Detailed characterization of Gleason parts and fibers.
Insights into the Svlov boundary structure.
Application of Aleksandrov and Hakim/Lw/Sibony's inner functions construction.
Abstract
We study the maximal ideal space of , where is the unit ball of . Following the lead of Gleason and Schark, we analyze Gleason parts, fibers, the S\u{\i}lov boundary, and other aspects of this Banach algebra. Our work here makes good use of the inner functions construction of Aleksandrov and Hakim/L{\o} w/Sibony, particularly as formulated by Rudin.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Advanced Harmonic Analysis Research
