Nonhomogeneous dual wavelet frames and mixed oblique extension principles in Sobolev spaces

ABSTRACT

From the literature, it is known that nonhomogeneous dual wavelet frames admit fast wavelet transform as homogeneous ones, and have more designing freedom than homogeneous ones. In this paper, we give a characterization of nonhomogeneous dual wavelet frames in $(H^s({\mathbb{R}}^d),H^{-s}({\mathbb{R}}^d))$, and using this characterization we derive a mixed oblique extension principle for such dual wavelet frames.

KEYWORDS:

• Frame
• nonhomogeneous dual wavelet frame
• Sobolev space

AMS SUBJECT CLASSIFICATIONS:

• 42C40
• 42C15

Acknowledgements

The authors cordially thank the referees for their careful reading and helpful comments which greatly improve the quality of this article.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11271037].