Fantappié transformations of analytic functionals on the sphere

Abstract

Let d be a positive integer and d ≧ 2. For K ⊂C d + 1 O(K) denotes the spaces of germs of holomorphic functions on K and O(K) denotes the dual spaces of O(K) The Fantappie indicator is defined by , where Pd + 1 (C) is the complex projective space of (d + 1) dimensions. A. Martineau determined the image of O(K) by the transformation Φ: T → Φ1 for the case where K is convex and compact. We consider the unit sphere S R d + 1. Martineau's result cannot apply for O′(S) because S is not convex. We will determine, in this paper, hte image of O′(S) by Φ.