The Cauchy dual subnormality problem (CDSP, for short) asks whether the Cauchy dual of a 2-isometry is subnormal. In this article, we provide a counter-example to CDSP by constructing a cyclic, analytic, 2-isometry whose defect operator is of rank 3. In particular, we prove that the Cauchy dual M_z' of the multiplication operator $M_z$ on the Dirichlet space D(μ) is not subnormal if μ is supported at three equi-spaced points on the unit circle.

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