ヒッツェル,エクハルト   HITZER, Eckhard
  ヒッツェル, エクハルト
   所属   国際基督教大学教養学部 アーツ・サイエンス学科
   職種   上級准教授
言語種別 英語
発行・発表の年月 2008
形態種別 研究論文(学術雑誌)
査読 査読あり
標題 Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4)
執筆形態 共著
掲載誌名 Adv. App. Cliff. Alg.
巻・号・頁 18(S 3,4),pp.715-736
担当範囲 Main part of text and computations.
著者・共著者 HITZER Eckhard, B. Mawardi
概要 First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions ( f:Rn→Cln,0,n=2,3 (mod 4)). Third, we show a set of important properties of the Clifford Fourier transform on Cl n,0, n = 2, 3 (mod 4) such as differentiation properties, and the Plancherel theorem, independent of special commutation properties. Fourth, we develop and utilize commutation properties for giving explicit formulas for fx m , f ∇ m and for the Clifford convolution. Finally, we apply Clifford Fourier transform properties for proving an uncertainty principle for Cl n,0, n = 2, 3 (mod 4) multivector functions.
DOI 10.1007/s00006-008-0098-3