The Riemann Hypothesis states that the non-trivial zeros of the Zeta function all have real part one-half. The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Zeta function corresponds to eigenvalues of an unbounded self-adjoint operator. There is only a formal representation of the Zeta function as transform of a Gaussian function based operator ((EdH) 10.3). The operator has no Mellin transform at all as the integrals do not converge due to the not vanishing constant Fourier term of the Gaussian. The original version (August 2015)
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