Abstract. We introduce some projection-invariants for a normalized sequence in a Hilbert space, based on the smallness of the mutual projections of its elements. We then establish conditions to have the original sequence equivalent to its Gram-Schmidt orthonormalization. In many problems of wavelet-decomposition and reconstruction, the use of orthogonal bases cannot be implemented in the construction of certain filters and other practical features. Then, a quasiorthonormal structure for representation may be the next best alternative by achieving new constraints while we can still arbitrarily approximate the powerful classical orthogonal results.
2000 Mathematics Subject Classification. 41A99, 65D99.
Key words and phrases. Quasiorthonormality, Gram-Schmidt operator, frame, wavelet.