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Heaviside function

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1: 1.16 Distributions
§1.16(iv) Heaviside Function
1.16.13 H ( x ) = { 1 , x > 0 , 0 , x 0 .
1.16.14 H ( x - x 0 ) = { 1 , x > x 0 , 0 , x x 0 .
1.16.44 sign ( x ) = 2 H ( x ) - 1 , x 0 ,
where H ( x ) is the Heaviside function defined in (1.16.13), and the derivatives are to be understood in the sense of distributions. …
2: 2.6 Distributional Methods
Furthermore, K + contains the distributions H , δ , and t λ , t > 0 , for any real (or complex) number λ , where H is the distribution associated with the Heaviside function H ( t ) 1.16(iv)), and t λ is the distribution defined by (2.6.12)–(2.6.14), depending on the value of λ . …
3: 1.14 Integral Transforms
1.14.22 f a + ( s ) = e - a s f ( s ) ,
where f a + ( t ) = H ( t - a ) f ( t - a ) and H is the Heaviside function; see (1.16.13). …