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Polynomial asymptotics and approximation of Sobolev functions. (English) Zbl 0823.46036

Summary: We prove several results concerning density of \(C^ \infty_ 0\), behaviour at infinity and integral representations for elements of the space \(L^{m, p}= \{f| \nabla^ m f\in L^ p\}\).

MSC:

46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
41A10 Approximation by polynomials
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A63 Multidimensional problems
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