Abstract
Every nontrivial zero of the Riemann zeta function is associated as eigenvalue with an eigenfunction of the fundamental differential operator on a Hilbert-Polya space. It has geometric multiplicity one. A relation between nontrivial zeros of the zeta function and eigenvalues of the convolution operator is given. It is an analogue of the Selberg transform in Selbergs trace formula. Elements of the Hilbert-Polya space are characterized by the Poisson summation formula.
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