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تسجيل مستخدم جديدHomomorphisms from Functional Equations: The Goldie Equation, II
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In this sequel to arXiv1407.4089 by the second author, we extend to multi-dimensional (or infinite-dimensional) settings the Goldie equation arising in the general regular variation of `General regular variation, Popa groups and quantifier weakening, J. Math. Anal. Appl. 483 (2020) 123610, 31 pp. (arXiv1901.05996). The theory focusses on extension of the treatment there of Popa groups, permitting a characterization of Popa homomorphisms (in two complementary theorems, 4A and 4B below). This in turn enables a characterization of the (real-valued) solutions of the multivariate Goldie equation, to be presented in the further sequel arXiv1910.05817. The Popa groups here contribute to a structure theorem describing Banach-algebra value
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In this the sequel to arXiv1910.05816, we derive a necessary and sufficient condition characterizing which real-valued continuous solutions of a multivariate Goldie functional equation express homomorphy between the multivariate Popa groups defined a
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