Strömberg wavelet

The term wavelet had not been coined at the time of publishing the discovery of Strömberg wavelet and Strömberg's motivation was to find an orthonormal basis for the Hardy spaces.

Let V be any discrete subset of the set R of real numbers.

For any r in V, let Ir denote the interval determined by V with r as the left endpoint.

[1] Let Sm be the Strömberg wavelet of order m. Then the following set is a complete orthonormal system in the space of square integrable functions over R. In the special case of Strömberg wavelets of order 0, the following facts may be observed: As already observed, the Strömberg wavelet S0(t) is completely determined by the set { S0(r) : r ∈ A1 }.

Using the defining properties of the Strömbeg wavelet, exact expressions for elements of this set can be computed and they are given below.