``Quasi''-norm of an arithmetical convolution operator and the order of the Riemann zeta function

@inproceedings{Hilberdink2013QuasinormOA,
  title={``Quasi''-norm of an arithmetical convolution operator and the order of the Riemann zeta function},
  author={Titus Hilberdink},
  year={2013}
}
In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = ni® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences… 

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