Homage \`{a} A. M. Gleason et I. J. Schark
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We study the maximal ideal space of $H^\infty(B)$, where $B$ is the unit ball of $\CC^n$. 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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