Questions tagged [tauberian-theorems]

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Relating $f(x)$ to its Laplace Transform for values other than $x=0$?

Suppose $X\in (0,1]$ is a random variable where $f(x)$ is its CDF and $g(t)$ is the Laplace Transform of $f(x)$. Tauberian theorems (Theorem 2.3 in Coqueret's "Approximation of probabilistic ...
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Bounds for PNT from Wiener-Ikehara?

What sort of bounds on the error term in the Prime Number Theorem can one obtain through a Wiener-Ikehara approach? Same question, but for the Mertens function $M(x)=\sum_{n\leq x} \mu(n)$.
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Can the Selberg-Delange method be extended to analyzing $\sum_{n<x}\frac{a_n}{n}$?

The famous Selberg-Delange method takes sequences $a_n$ whose associated DGF $F(s)=\sum_{n=1}^{\infty}\frac{a_n}{n^s}$ has a representation $$F(s)=G(s;z)\zeta^z(s)$$ where $G(s;z)$ is "nice ...
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Reference needed for proof of a Tauberian theorem

I was reading the following paper by Hubert Delange: http://www.numdam.org/article/ASENS_1956_3_73_1_15_0.pdf 1. In page 26, he provides a proof of Theorem b, the bulk of which relies on a result in ...
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Dense stratification of a separable Hilbert space

Let $\{X_i\}_{i \in \mathbb{N}}$ be a sequence of $n$-dimensional linear subspaces of the separable Hilbert space $H$ and let $\{\phi_i\}_{i \in I}$ be a sequence of continuous injective linear maps ...
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Weak version of Karamata's Tauberian theorem

I first posted this on mathematics. However, I got no answer there and it seems adapted here too. Also, it seems to be harder than I first thought. Karamata's Tauberian theorem states the following. ...
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