# How to introduce not-orthonormal base on Reproducing Kernel Hilbert Spaces?

I read some tutorial papers and slide，and find that the bases on Reproducing Kernel Hilbert Spaces always be orthonormal. For examples，you can refer to this link for the content about Reproducing Kernel Hilbert Spaces. What if the introduced base are not orthonormal? Any papers talk about this problems?

• You need to be careful about what you mean by a "basis" when dealing with infinite-dimensional normed spaces: there are several different notions, and I think you should first look up which one fits your needs. Right now, since it is not clear if you know what a Schauder basis or an unconditional basis is, it is difficult to point you in an appropriate direction – Yemon Choi Jul 28 '20 at 13:57
• In any case, if you are relatively inexperienced in mathematics, then perhaps you would do better to ask your question on math.stackexchange.com – Yemon Choi Jul 28 '20 at 13:57
• @YemonChoi, thanks for your comments. You can check the link I refer in my questions. What makes I confuse is that if I introduce a non-orthonormal to replace the basis e_m in Eq.(1) mentioned in the link. Then, if the kernel still has the original property like: 𝑓(𝑎)=⟨𝑓,𝐾𝑎⟩ – Max Jul 29 '20 at 8:00