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On the convergence of the series \( \sum_ 1^ \infty{} a_ m \exp - < \lambda{}_ m , \Psi{} (x) > \). (English) Zbl 0749.40004

The series in the title are series of exponential functions of several variables, and the results obtained are of the following type: If the series converges for some \(x_ j=x^ 0_ j\), \(j=1,\dots,n\), then it converges uniformly for every \(\Psi_ j(x_ j)>\Psi_ j(x^ 0_ j)\), \(j=1,\dots,n\).

MSC:

40A30 Convergence and divergence of series and sequences of functions
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