\mathbb{R^+_*} refers to the set of positive real numbers, excluding zero. In the context of "Wavelets on the 2-Sphere", it is often used to represent the scale parameter in wavelet analysis.
The 2-sphere is a non-Euclidean space, meaning the usual Euclidean geometry and notation does not apply. Therefore, special notation is needed to represent certain mathematical concepts, such as the scale parameter in wavelet analysis.
Yes, there are alternative notations that can be used to represent the scale parameter in wavelet analysis on the 2-sphere, such as the set of positive real numbers with an asterisk (\mathbb{R}^+_{\ast}) or the interval [0, ∞). However, \mathbb{R^+_*} is commonly used and understood in the context of wavelet analysis on the 2-sphere.
\mathbb{R^+_*} is used to represent the scale parameter in the dilation equation of wavelet analysis on the 2-sphere. It is also used to define the support of wavelet functions, which is essential in constructing wavelet transforms on the 2-sphere.
Yes, depending on the specific context and notation conventions, variations of \mathbb{R^+_*} may be used, such as \mathbb{R}^+ or \mathbb{R}^+_{>0}. However, the concept of representing the set of positive real numbers remains the same in all variations of notation.