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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:

[1] [1] -, Linear Operators, Part I: General Theory; Part II: Spectral Theory. New York: Interscience 1958, 1963. · Zbl 0084.10402
[2] GOHBERG, KREJN, Introduction à la théorie des opérateurs non auto-adjoints dans un espace hilbertien, Monographies universitaires de Mathématiques n° 39, Dunod.
[3] J. ECALLE, Well-behaved convolution averages and their application to real resummation, à paraître, première partie parue dans [5].
[4] J. ECALLE et F. MENOUS, Well-behaved convolution averages and the non-accumulation theorem for limit-cycles, Prépublication d’Orsay, 1995.0857.34009 · Zbl 0857.34009
[5] T. KATO, Pertubation theory for linear operators, Springer Verlag, 1966.0148.12601 · Zbl 0148.12601
[6] [6] , Les bonnes moyennes uniformisantes et leurs applications à la resommation réelle, Thèse, Paris XI Orsay, 1996. · Zbl 0972.40001
[7] F. SMITHIES, Integral equations, Cambridge University Press, 1970. · Zbl 0082.31901
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