Localization Operators on Quaternionic Hilbert Spaces

摘要

In this paper, we study the localization operator associated to quaternionic continuous wavelet transform. We show that the quaternionic localization operator is bounded if the continuous wavelet transform is real valued. Also, we investigate the relation between the localization operators in the setting of quaternion and complex Hilbert spaces. Furthermore, we prove that the quaternionic two-wavelet localization operator is bounded under some conditions.