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I will give a survey of the operator theory that is currently evolving on Hardy spaces of Dirichlet series. We will consider recent results about multiplicative Hankel operators as introduced and studied by Helson and developments building on the Gordon-Hedenmalm theorem on bounded composition operators on the $H^2$ space of Dirichlet series.

47B35 ; 30B50 ; 30H10

Starting with a personal tribute to Victor Havin (1933-2015), I discuss a dozen achievements of Great Havin's Analysis Seminar, as well as some challenging still unsolved problems.
The Havin publications list is available in the PDF file at the bottom of the page.

30H10 ; 01A60 ; 01A70

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