Resumen de Principal shift-invariant spaces with extra invariance nearest to observed data

Akram Aldroubi, Ilya A. Krishtal, Romain Tessera, Haichao Wang

• Given a set of functions ={?1,…,??}⊂?2(ℝ), we construct a principal shift-invariant space V nearest to in the sense that V minimizes the expression ∑?=1?‖??−????‖2, among all the principal shift-invariant spaces with an orthonormal generator which are also translation invariant, or among all the principal shift-invariant spaces with an orthonormal generator which are also 1?ℤ -invariant for some fixed ?∈ℕ .