Premium
Sharper uncertainty principles in quaternionic Hilbert spaces
Author(s) -
Xu Zhenghua,
Ren Guangbin
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5988
Subject(s) - quaternion , mathematics , operator (biology) , hilbert space , pure mathematics , commutator , fourier transform , fock space , algebra over a field , mathematical analysis , geometry , quantum mechanics , biochemistry , chemistry , lie conformal algebra , physics , repressor , transcription factor , gene
The uncertainty principle for quaternionic linear operators in quaternionic Hilbert spaces is established, which generalizes the result of Goh‐Micchelli. It turns out that there appears an additional term given by a commutator that reflects the feature of quaternions. The result is further strengthened when one operator is self‐adjoint, which extends under weaker conditions the uncertainty principle of Dang‐Deng‐Qian from complex numbers to quaternions. In particular, our results are applied to concrete settings related to quaternionic Fock spaces, quaternionic periodic functions, quaternion Fourier transforms, quaternion linear canonical transforms, and nonharmonic quaternion Fourier transforms.