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Dimension functions, scaling sequences, and wavelet sets

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Ljiljana A., Bakić D., Rajić R.

Studia Mathematica

2010

tom 198

nr 1

1-32

The paper is a continuation of our study of dimension functions of orthonormal wavelets on the real line with dyadic dilations. The main result of Section 2 is Theorem 2.8 which provides an explicit reconstruction of the underlying generalized multiresolution analysis for any MSF wavelet. In Section 3 we reobtain a result of Bownik, Rzeszotnik and Speegle which states that for each dimension function D there exists an MSF wavelet whose dimension function coincides with D. Our method provides a completely new explicit construction of an admissible generalized multiresolution analysis (and, a posteriori, of a wavelet) from an arbitrary dimension function. Several examples are included.

Ograniczanie wyników

1 Studia Mathematica

1 Bakić D.

1 Ljiljana A.

1 Rajić R.

1 2010

Wyniki wyszukiwania

Dimension functions, scaling sequences, and wavelet sets