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Null Function

A null function delta^0(x) satisfies

int_a^bdelta^0(x)dx=0
(1)

for all a,b, so

int_(-infty)^infty|delta^0(x)|dx=0.
(2)

Like a delta function, they satisfy

delta^0(x)={0 x!=0; 1 x=0.
(3)

See also

Delta Function, Lerch's Theorem

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References

Bracewell, R. "Null Functions." In The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 82-84, 1999.

Referenced on Wolfram|Alpha

Null Function

Cite this as:

Weisstein, Eric W. "Null Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NullFunction.html

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