Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces

摘要: Abstract This paper devotes to studying uncertainty principles of Heisenberg type for signals defined on R n taking values in a Clifford algebra. For real-para-vector-valued possessing all first-order partial derivatives we obtain two which both correspond the strongest form one-dimensional space. The lower-bounds new are terms scalar-valued phase derivative. Through Hardy spaces decomposition also forms real-valued finite energy with first order Sobolev smoothness.