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Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur

Electronic Theses and Dissertations

In this paper we present a survey of results on the Schrodinger operator with Inverse ¨ Square potential, L_a= −∆ + a/|x|^2 , a ≥ −( d−2/2 )^2. We briefly discuss the long-time behavior of solutions to the inter-critical focusing NLS with an inverse square potential(proof not provided). Later we present spectral multiplier theorems for the operator. For the case when a ≥ 0, we present the multiplier theorem from Hebisch [12]. The case when 0 > a ≥ −( d−2/2 )^2 was explored in [1], and their proof will be presented for completeness. No improvements on the sharpness …