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The Banach Algebra of Bounded ϕ-Variation Functions on Compact Subsets of ℂ

Abstract:

A concept of generalized bounded ϕ−variation for complex-valued functions is introduced. We prove that the space of functions of this kind is a Banach algebra with respect to pointwise multiplication. Previously, its properties were shown and the Minkowski functional was used to provide this class of functions with a norm that makes it a Banach space. In addition, some maximal ideals are described.