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:
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