Coefficient estimates for exponential series

Sledd, W. T.

doi:10.1090/S0002-9939-1974-0349970-5

Coefficient estimates for exponential series
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by W. T. Sledd PDF

Proc. Amer. Math. Soc. 45 (1974), 357-364 Request permission

Abstract:

Results are obtained which relate the size of the coefficients ${a_n}$ of an exponential series $f(x) = \Sigma _{n = 0}^\infty {a_n}{\varepsilon ^{ - {\Lambda _n}x}},x > 0,\operatorname {Re} {\Lambda _n} > 0$, to the function $f$. These results involve comparisons between weighted ${l^p}$ sums of the sequence $({a_n})$ and weighted ${L^p}$ integrals of $f$ on $[0,\infty )$.

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