## Étude d’une fonction remarquable associée aux moyennes de convolution. (Study of a remarkable function associated to convolution averages.).(French)Zbl 0921.47003

Summary: In this article we study the generating series of alternating weights of a convolution-preserving average induced by diffusion. We prove that it is a meromorphic function, naturally associated to a particular compact operator. This function is equal to $$d(-z)/d(z)$$, whenever the Fredholm determinant $$d(z)$$ of this operator exists, and we precise it in other cases.

### MSC:

 47A10 Spectrum, resolvent 47G10 Integral operators 45B05 Fredholm integral equations 47A53 (Semi-) Fredholm operators; index theories
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### References:

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