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Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions

Lower bounds for resonance counting functions for Schrödinger operators with fixed sign potentials in even dimensions

If d is even, the resonances of the Schrödinger operator -\Delta +V on \mathbb R^d with V\in L^{infty}_{\mathrm {comp}}(\mathbb R^d) are points on \Lambda , the logarithmic cover of \mathbb C \setminus \{0\} . We show that for fixed sign potentials V and for m\in \mathbb Z \setminus \{0\} , …