Abstract
In this paper, we provide a geometric construction of a symmetric 2n-interval minimally supported frequency (MSF) d-dilation wavelet set with d∈(1,∞) and characterize all symmetric d-dilation wavelet sets. We also provide two special kinds of symmetric d-dilation wavelet sets, one of which has 4m-intervals whereas the other has (4m+2)-intervals, for m∈N. In addition, we construct a family of d-dilation wavelet sets that has an infinite number of components.
Highlights
minimally supported frequency (MSF) d-dilation wavelets arising from these d-dilation wavelet sets are band-limited, and their Fourier transform is even and does not vanish in any neighborhood of origin, i.e., it was discontinuous at the origin
We provide two special kinds of symmetric d-dilation wavelet sets with d > 1, one of which has 4m-intervals, whereas the other has (4m + 2)-intervals, where m ∈ N
To obtain that Ke is a d-dilation wavelet set, we show that Ke+ is both translation- and d-dilation-equivalent to K + constructed in Example 4
Summary
We provide a family of six-interval d-dilation wavelet sets and two special kinds of symmetric d-dilation wavelet sets, one of which has 4m intervals, whereas the other has (4m + 2) intervals, where m ∈ N. The d-dilation wavelet set constructed is bounded symmetric d-dilation wavelet sets having infinite number of components, and the accumulation point of these wavelet sets is their origin. MSF d-dilation wavelets arising from these d-dilation wavelet sets are band-limited, and their Fourier transform is even and does not vanish in any neighborhood of origin, i.e., it was discontinuous at the origin
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