Gauss iterated map

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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, is the space of distributions, is the space of tempered distributions in , the differentiation operator with a multi-index, and is the Fourier transform of .

The Beppo-Levi space is
( denotes the Sobolev semi-norm)

An alternative definition is:

Given such that

Let

Then denotes the Beppo-Levi space

References

  • 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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