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Zeros and regular growth of Laplace transforms along curves. (English) Zbl 0733.44001
We extend some results of Müntz-Szász type due to Korevaar and Leont’ev: Let $$\gamma (t)=t+i$$ h(t), $$0\leq t<\infty$$, be a Lipschitz curve and let $$(\lambda_ n)$$ be an increasing sequence of positive numbers such that $$\sum \lambda_ n^{-1}=\infty$$. Then, under a technical additional condition on $$\gamma$$ which is satisfied if h(t) is piecewise $$C^ 1$$ or piecewise monotone, the exponentials $$\exp (- \lambda_ nz)$$ span $$C_ 0(\gamma)$$. More generally, a Blaschke type convergence condition is given for the zeros of Laplace transforms of measures supported on $$\gamma$$, and it is shown that these Laplace transforms are of very regular growth in the sense of Ahlfors-Heins- Azarin.
Reviewer: R.Zeinstra

##### MSC:
 44A10 Laplace transform
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