{
  "id": "1511.09276",
  "version": "v1",
  "published": "2015-11-30T12:43:57.000Z",
  "updated": "2015-11-30T12:43:57.000Z",
  "title": "Homomorphisms between algebras of $\\mathcal F$-differentiable functions",
  "authors": [
    "T. Chaobankoh",
    "J. F. Feinstein",
    "S. Morley"
  ],
  "comment": "12 pages, submitted",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $X$ be a perfect, compact subset of the complex plane, and let $D^{(1)}(X)$ denote the (complex) algebra of continuously complex-differentiable functions on $X$. Then $D^{(1)}(X)$ is a normed algebra of functions but, in some cases, fails to be a Banach function algebra. Bland and the second author investigated the completion of the algebra $D^{(1)}(X)$, for certain sets $X$ and collections $\\mathcal{F}$ of paths in $X$, by considering $\\mathcal{F}$-differentiable functions on $X$. In this paper, we investigate composition, the chain rule, and the quotient rule for this notion of differentiability. We also investigate homomorphisms between certain algebras of $\\mathcal{F}$-differentiable functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-30T12:43:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46J10",
      "46J15",
      "46E25"
    ],
    "keywords": [
      "homomorphisms",
      "banach function algebra",
      "complex plane",
      "compact subset",
      "second author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151109276C"
    }
  }
}