This paper develops a technique to represent linear functionals on spaces of homogeneous polynomials between Banach spaces. This technique applies to cases that are not covered by the classical polynomial Borel transform. We provide applications to represent linear functionals on spaces of approximable, compact, hyper-nuclear and hyper-\(\sigma (p)\)-nuclear polynomials. An unexpected difference between the polynomial and multilinear theories is disclosed.

中文翻译：

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多项式 Hyper-Borel 变换

本文开发了一种在 Banach 空间之间的齐次多项式空间上表示线性泛函的技术。此技术适用于经典多项式 Borel 变换未涵盖的情况。我们提供了在可近似、紧致、超核和超- \(\sigma (p)\)-核多项式空间上表示线性泛函的应用程序。揭示了多项式理论和多重线性理论之间的意外差异。