Term of Award
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
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This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Mathematical Sciences
Committee Member 1
Committee Member 2
In this paper we present a survey of results on the Schrodinger operator with Inverse ¨ Square potential, La= −∆ + 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 . The case when 0 > a ≥ −( d−2/2 )^2 was explored in , and their proof will be presented for completeness. No improvements on the sharpness of their proof as been obtained.
Saint Bonheur, Richardson, "Survey of Results on the Schrodinger Operator with Inverse Square Potential" (2018). Electronic Theses and Dissertations. 1847.
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