Original scientific paper

Projection-invariants, Gram-Schmidt operators, and wavelets

Jean-Paul Pemba

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.

Keywords

Quasiorthonormality; Gram-Schmidt operator; frame; wavelet

Hrčak ID:

1324

URI

https://hrcak.srce.hr/1324

Publication date:

1.12.2003.

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