For the HAAR wavelet is the first developed wavelet, I suggest you to view Schauder Base
And this papers:
Chen, C. F., & Hsiao, C. H. (1997, January). Haar wavelet method for solving lumped and distributed-parameter systems. In Control Theory and Applications, IEE Proceedings- (Vol. 144, No. 1, pp. 87-94). IET.
Lai, Y. K., & Kuo, C. C. J. (2000). A Haar wavelet approach to compressed image quality measurement. Journal of Visual Communication and Image Representation, 11(1), 17-40.