The following problem was posed by Olson and Zalik in 1992:
Does there exist a function f ∈ L2(R) such that some system of its translates forms a Schauder basis in L2(R)?
This problem remains unsolved, as well as its counterpart for Lp(R) spaces. We will discuss certain related results, in particular we will concentrate on the question of existence of Schauder frames (which are, roughly speaking, coordinate systems in Banach spaces that need not be minimal) of translates.
The talk is based on the (recent and partly ongoing) joint work with Nir Lev.
https://univienna.zoom.us/j/67922750549?pwd=Ulh5L1QxNFhBOC9PUjlVdG9hc0tmUT09