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caz

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caz

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marcusl

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- Arfken, Mathematical Methods for Physicists
- Bracewell, The Fourier Transform and Its Applications
- Dirac, The Principles of Quantum Mechanics (of course!)

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BvU

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I wonder what you would consider a proof of a representation . A delta function is a something with certain well described properties. The word distributions comes to mind (out of the dust of ages). Showing that the representation exhibits such properties is just that: a showing.representations of the delta function. Is there a place/reference that lists AND proves them

[Links added after commenting; plenty references for further study. As a physicist I'm comfortable with 'infinitely narrow and high needle with area 1' but I would never claim that would prove anything]

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caz

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WWGD

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What are the properties you refer to?

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caz

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S.G. Janssens

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The best way (avoiding magic) to manipulate ##\delta##-functions or, generally, distributions, is by first pairing with an arbitrary (i.e. smooth, compactly supported) test function, doing the manipulations (usually involving partial integration) and limits in ##\mathbb{R}## and then, at the end, concluding that a certain identity, or limit representation holds true for the distributions in question, because the test function was chosen arbitrarily.

Any introduction to (or: containing material about) distribution theory will show you this in detail, while keeping the underlying functional analysis out, or to a minimum, so it is accessible to physicists with a good background in multivariable calculus. There is the book by Strichartz and the book by Duistermaat and Kolk, for example.

Any introduction to (or: containing material about) distribution theory will show you this in detail, while keeping the underlying functional analysis out, or to a minimum, so it is accessible to physicists with a good background in multivariable calculus. There is the book by Strichartz and the book by Duistermaat and Kolk, for example.

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caz

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I’ll give Strichartz a try. Thanks.

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