Haar bases for L²(Q₂²) generated by one wavelet function

الأصل · EN

The concept of p-adic quincunx Haar MRA was introduced and studied in KS10. In contrast to the real setting, infinitely many different wavelet bases are generated by a p-adic MRA. We give an explicit description for all wavelet functions corresponding to the quincunx Haar MRA. Each one generates an orthogonal basis, one of them was presented in KS10. A connection between quincunx Haar bases and two-dimensional separable Haar MRA is also found.