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Giorgio Metafune
Giorgio Metafune
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Let me answer to the second question, which is the motivation for the first. The precise description of the domain of Schroedinger operator with inverse square potential in the critical case is known and can be found in Proposition 4.3 of https://arxiv.org/abs/2103.10314. From this it follows that functions in the maximal domain for which $u(r) \leq Cr^{t_+}$$|u(r)| \leq Cr^{t_+}$ lye in the domain. In Examples 7/2, 7.3 in https://arxiv.org/abs/1405.5657 it is also proved that this domain is the Friedrichs extension of your operator.

Let me answer to the second question, which is the motivation for the first. The precise description of the domain of Schroedinger operator with inverse square potential in the critical case is known and can be found in Proposition 4.3 of https://arxiv.org/abs/2103.10314. From this it follows that functions in the maximal domain for which $u(r) \leq Cr^{t_+}$ lye in the domain. In Examples 7/2, 7.3 in https://arxiv.org/abs/1405.5657 it is also proved that this domain is the Friedrichs extension of your operator.

Let me answer to the second question, which is the motivation for the first. The precise description of the domain of Schroedinger operator with inverse square potential in the critical case is known and can be found in Proposition 4.3 of https://arxiv.org/abs/2103.10314. From this it follows that functions in the maximal domain for which $|u(r)| \leq Cr^{t_+}$ lye in the domain. In Examples 7/2, 7.3 in https://arxiv.org/abs/1405.5657 it is also proved that this domain is the Friedrichs extension of your operator.

Source Link
Giorgio Metafune
Giorgio Metafune
  • 6k
  • 2
  • 9
  • 20

Let me answer to the second question, which is the motivation for the first. The precise description of the domain of Schroedinger operator with inverse square potential in the critical case is known and can be found in Proposition 4.3 of https://arxiv.org/abs/2103.10314. From this it follows that functions in the maximal domain for which $u(r) \leq Cr^{t_+}$ lye in the domain. In Examples 7/2, 7.3 in https://arxiv.org/abs/1405.5657 it is also proved that this domain is the Friedrichs extension of your operator.