2007 | OriginalPaper | Buchkapitel
Uncertainty Principle for Clifford Geometric Algebras Cl n,0, n = 3 (mod 4) Based on Clifford Fourier Transform
verfasst von : Eckhard S. M. Hitzer, Bahri Mawardi
Erschienen in: Wavelet Analysis and Applications
Verlag: Birkhäuser Basel
Aktivieren Sie unsere intelligente Suche um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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
: ℝ
n
→
Cl
n
,0
,
n
= 3 (mod 4)). Third, we introduce a set of important properties of the Clifford Fourier transform on
Cl
n
,0
,
n
= 3 (mod 4) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving a directional uncertainty principle for
Cl
n
,0
n
= 3 (mod 4) multivector functions.