## On multiplication of some generalized functions.(English)Zbl 0961.46032

Summary: We show that if we extend the classical definition of a product of functions to a larger class of distributions, then for the distributions of the form $${1\over(\cdot-i0)^\alpha}$$ and $${1\over (\cdot+i0)^\alpha}$$, where $$\alpha$$ is complex number, we get formulas: ${1\over (\cdot-i0)^\alpha}\cdot {1\over (\cdot- i0)^\beta}= {1\over (\cdot- i0)^{\alpha+\beta}}$ and ${1\over (\cdot+ i0)^\alpha}\cdot {1\over (\cdot+ i0)^\beta}= {1\over (\cdot+ i0)^{\alpha+ \beta}},$ when $$\alpha$$ and $$\beta$$ are complex numbers, such that $$\text{Re }\alpha> {1\over 2}$$ and $$\text{Re }\beta> {1\over 2}$$.

### MSC:

 46F10 Operations with distributions and generalized functions 46F12 Integral transforms in distribution spaces 44A15 Special integral transforms (Legendre, Hilbert, etc.) 44A20 Integral transforms of special functions
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### References:

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