Abstract
We will now introduce test functions and do so by specializing the testing of f as in (1.12). If we set x = 0 and replace \(\phi (y)\ {\rm by}\ \phi ( - y),\) the result of testing f by means of the weight function becomes equal to the “integral inner product” \(\left\langle {f,\phi } \right\rangle = \int_R {f(x)\phi (x)\,dx.}\)
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Duistermaat, J.J., Kolk, J.A.C. (2010). Test Functions. In: Distributions. Cornerstones. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4675-2_2
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DOI: https://doi.org/10.1007/978-0-8176-4675-2_2
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Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4672-1
Online ISBN: 978-0-8176-4675-2
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