Please excuse my english. I have had the following math courses for mechatronics engineering education:
- Calculus (single and multivariable)
- Linear algebra (introductory)
- Differential equations (ode's and introductory pde's + Fourier series)
As I read Mallat's paper "A theory for Multiresolution Signal Decomposition", I realize that there are gaps in my mathematical understanding of the content. I feel as if I read a poem without catching the meaning between the lines.
PS, I love mathematics and often spend time self-educating myself further than that what is required for the education program.
The theory of wavelets is a broad field, but looking at your background and the paper you mention I think the book Funtions, Spaces and Expansions by Ole Christensen covers everything you need to know.
The prerequisites for reading this book are linear algebra and elementary analysis. The book introduces basic concepts as normed spaces, Hilbert spaces and $L^p$ spaces, and it finishes with a discussion on multiresolution analysis.