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Beppo-Levi space

From Wikipedia, the free encyclopedia

In functional analysis, a branch of mathematics, a Beppo Levi space, named after Beppo Levi, is a certain space of generalized functions.

In the following, D′ is the space of distributions, S′ is the space of tempered distributions in Rn, Dα the differentiation operator with α a multi-index, and is the Fourier transform of v.

The Beppo Levi space is

where |⋅|r,p denotes the Sobolev semi-norm.

An alternative definition is as follows: let mN, sR such that

and define:

Then Xm,s is the Beppo-Levi space.

References

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  • Wendland, Holger (2005), Scattered Data Approximation, Cambridge University Press.
  • Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" Numerische Mathematik
  • Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2009), "Estimates for functions in Sobolev spaces defined on unbounded domains" Journal of Approximation Theory
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