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 2013
形態種別 会議報告等
査読 査読あり
標題 The orthogonal planes split of quaternions
執筆形態 共著
掲載誌名 Trends in Mathematics 27, Birkhauser, Basel, 2013, pp. 15-39. DOI: 10.1007/978-3-0348-0603-9_2
掲載区分国外
出版社・発行元 Birkhauser, Basel, Switzerland.
巻・号・頁 pp.15-39
担当範囲 Symbolic algebraic computations and part of text.
著者・共著者 HITZER Eckhard, S. J. Sangwine
概要 The two-sided quaternionic Fourier transformation (QFT) was introduced in [2] for the analysis of 2D linear time-invariant partial-differential systems. In further theoretical investigations [3, 4] a special split of quaternions was introduced, then called plus minus split. In the current paper we analyze this split further, interpret it geometrically as orthogonal planes split (OPS), and generalize it. The new general form of the OPS split allows us to find new geometric interpretations for the action of the QFT on the signal. The second major result of this work is a variety of new forms of the QFT, their geometric interpretation, and for each form OPS split theorems, which allow fast and efficient numerical implementation with standard FFT software.
DOI 10.1007/978-3-0348-0603-9_2