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- W2904685099 abstract "We present quantitative versions of Bohr's theorem on general Dirichlet series $D=sum a_{n} e^{-lambda_{n}s}$ assuming different assumptions on the frequency $lambda:=(lambda_{n})$, including the conditions introduced by Bohr and Landau. Therefore using the summation method by typical (first) means invented by M. Riesz, without any condition on $lambda$, we give upper bounds for the norm of the partial sum operator $S_{N}(D):=sum_{n=1}^{N} a_{n}(D)e^{-lambda_{n}s}$ of length $N$ on the space $mathcal{D}_{infty}^{ext}(lambda)$ of all somewhere convergent $lambda$-Dirichlet series allowing a holomorphic and bounded extension to the open right half plane $[Re>0]$. As a consequence for some classes of $lambda$'s we obtain a Montel theorem in $mathcal{D}_{infty}(lambda)$; the space of all $D in mathcal{D}_{infty}^{ext}(lambda)$ which converge on $[Re>0]$. Moreover following the ideas of Neder we give a construction of frequencies $lambda$ for which $mathcal{D}_{infty}(lambda)$ fails to be complete." @default.
- W2904685099 created "2018-12-22" @default.
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- W2904685099 date "2018-12-12" @default.
- W2904685099 modified "2023-09-27" @default.
- W2904685099 title "On Bohr's theorem for general Dirichlet series." @default.
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