Schwartz Space

The set of all Schwartz functions is called a Schwartz space and is denoted S(R^n). If C_0^infty(R^n) denotes the set of smooth functions of compact support on R^n, then this is a subset of S(R^n). Since C_0^infty(R^n) is dense in L^p(R^n), S(R^n) is dense in L^p(R^n) for any p>=1.

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This entry contributed by W.D. Van Suijlekom

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

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