Disk Algebra

A disk algebra is an algebra of functions which are analytic on the open unit disk in C and continuous up to the boundary. A representative measure for a point x in the closed disk is a nonnegative measure m such that Int(fdm)=f(x) for all f in A. These measures form a compact, convex set M_x in the linear space of all measures.

Stated another way, let Delta denote the closed unit disk {z in C:|z|<=1}. Suppose that A(Delta) denoted the set of all elements of C(Delta) which are analytic on the interior of Delta. A(Delta) is a closed subalgebra of C(Delta) and so is a unital commutative Banach algebra. This algebra is called the disk algebra.

See also

Portions of this entry contributed by Ronald M. Aarts

Portions of this entry contributed by Mohammad Sal Moslehian

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Aarts, Ronald M.; Moslehian, Mohammad Sal; and Weisstein, Eric W. "Disk Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DiskAlgebra.html

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