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Schwartz Space

The Schwartz space S(R^n) is the set of all Schwartz functions. If C_0^infty(R^n) denotes the set of C∞ functions of compact support on R^n, then this is a subset of S(R^n) (Hunter 2014, p. 166). Since C_0^infty(R^n) is dense in Lp(Rn), S(R^n) is dense in Lp(Rn) for 1<=p<infty (Hunter 2014, p. 12).

See also

Schwartz Function

This entry contributed by W.D. Van Suijlekom

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References

Hunter, J. K. Notes on Partial Differential Equations. Jun. 18, 2014. https://math.ucdavis.edu/~hunter/pdes/pde_notes.pdf.

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Schwartz Space

Cite this as:

Weisstein, Eric W., with contributions by W.D. Van Suijlekom. "Schwartz Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchwartzSpace.html

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