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- W2150577985 abstract "In this chapter, we study approximations of the identity on $${mathbb{R}}^{D}$$ with the measures μ satisfying (0.0.1). To this end, we first introduce an important notion of coefficients δ(Q, R) for cubes Q and R in $${mathbb{R}}^{D}$$ . It turns out that δ(Q, R) characterizes the geometric relationship between Q and R. Using this notion, we further study cubes of different generations in terms of δ(Q, R), which are versions of dyadic cubes in the setting $$({mathbb{R}}^{D},vert cdot vert,mu )$$ . Then we construct the functions, $${f_{y,,k}}_{yin mathrm{,supp,}mu, kin mathbb{Z}}$$ , which originate the kernels of approximations of the identity. Via these functions, we introduce and establish some important properties of the approximations of the identity on $${mathbb{R}}^{D}$$ ." @default.
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- W2150577985 date "2013-01-01" @default.
- W2150577985 modified "2023-09-25" @default.
- W2150577985 title "Approximations of the Identity" @default.
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- W2150577985 doi "https://doi.org/10.1007/978-3-319-00825-7_2" @default.
- W2150577985 hasPublicationYear "2013" @default.
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