Abstract—In this article, partial affine system-based frames is studied. We obtain some inequalities in form of matrix for a partial affine system to be a partial affine frame in the setting of subspaces of L²(ℝ). The results improve known ones by W. Sun, Chui, Shi, and Chen, Ron and Shen.

Index Terms—Frame, wavelet frame, partial affine system.

The author is with College of Applied Sciences, Beijing University of Technology, Pingle Yuan 100, Beijing, 100124, P. R. China (email: yutian@emails.bjut.edu.cn).

Cite: Yu Tian, "A Note on the Inequalities for Partial Affine System-Based Frames," International Journal of Applied Physics and Mathematics vol. 7, no. 4, pp. 284-290, 2017.