Abstract
Contemporary investigations in the theory of nonlinear integral operators ([9], [10]) and in the differential calculus ([5], [11]) have led to generalizations of the notion of a polynomial map between two vector spaces. This article studies basic properties of such so-called polyhomogeneous maps. Our initial point of reference is the recent study of polynomial maps by Bochnak and Siciak [2]. Our examination of continuity properties leads to new characterizations of braked spaces and sequential spaces. Then, we turn to the polyhomogeneous approximating maps studied by Melamed and Perov [9] and Moore and Nashed [10]. We present some generalizations of the results of [9] and [10] and then go on to study permanence properties of such approximations.
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Findley, D.F. Polyhomogeneous maps and best local approximations of degree α. Manuscripta Math 15, 1–31 (1975). https://doi.org/10.1007/BF01168876
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DOI: https://doi.org/10.1007/BF01168876