Are Products of Dirac Delta Functions Well-Defined?

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The discussion centers on the well-defined nature of products involving Dirac delta functions. It highlights that the Dirac delta is a distribution rather than a conventional function, which complicates multiplication between distributions. Specifically, the products δ(z*-z0*)δ(z+z0) and δ(z*+z0*)δ(z-z0) lack clear meaning and are not well-defined. The consensus is that while distributions can be multiplied by smooth functions, multiplying one distribution by another is generally not permissible. Therefore, the expressions presented do not hold a valid mathematical interpretation.
Muthumanimaran
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Homework Statement



δ(z*-z0*)δ(z+z0)=?
δ(z*+z0*)δ(z-z0)=?

where 'z' is a complex variable 'z0' is a complex number
Formula is just enough, derivation is not needed.
 
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The Dirac delta is a distribution, not a number or a function from one number field to another.
The product of distributions is not in general well defined, see here. You can multiply a distribution by a smooth function, but not in general by another distribution.
So the expressions above do not have a clear meaning. They are not well-defined.
 

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