On the eigenvalue counting function for Schrödinger operator: some upper bounds
The aim of this work is to provide an upper bound on the eigenvalues counting function N(Rn, −∆+V, e) of a Schr¨odinger operator −∆+V on R^n corresponding to a potential V ∈ L^(n/2 +ε) (Rn, dx), in terms of the sum of the eigenvalues counting function of the Dirichlet integral D with Dirichlet bound...
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Sapienza Università Editrice
2018-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | http://www1.mat.uniroma1.it/ricerca/rendiconti/39_2_(2018)_257-276.html |
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doaj-f163ce49b54b4ee9b6b2c3556fcb19f42020-11-25T02:47:17ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502018-01-0139257276On the eigenvalue counting function for Schrödinger operator: some upper boundsFabio Cipriani0Dipartimento di Matematica, Politecnico di MilanoThe aim of this work is to provide an upper bound on the eigenvalues counting function N(Rn, −∆+V, e) of a Schr¨odinger operator −∆+V on R^n corresponding to a potential V ∈ L^(n/2 +ε) (Rn, dx), in terms of the sum of the eigenvalues counting function of the Dirichlet integral D with Dirichlet boundary conditions on the subpotential domain {V < e}, endowed with weighted Lebesgue measure (V − e)− · dx and the eigenvalues counting function of the absorption-to-reflection operator on the equipotential surface {V = e}.http://www1.mat.uniroma1.it/ricerca/rendiconti/39_2_(2018)_257-276.htmlSchr¨odinger operatorseigenvalues counting functionDirichlet-to-Neumann operator |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Fabio Cipriani |
| spellingShingle |
Fabio Cipriani On the eigenvalue counting function for Schrödinger operator: some upper bounds Rendiconti di Matematica e delle Sue Applicazioni Schr¨odinger operators eigenvalues counting function Dirichlet-to-Neumann operator |
| author_facet |
Fabio Cipriani |
| author_sort |
Fabio Cipriani |
| title |
On the eigenvalue counting function for Schrödinger operator: some upper bounds |
| title_short |
On the eigenvalue counting function for Schrödinger operator: some upper bounds |
| title_full |
On the eigenvalue counting function for Schrödinger operator: some upper bounds |
| title_fullStr |
On the eigenvalue counting function for Schrödinger operator: some upper bounds |
| title_full_unstemmed |
On the eigenvalue counting function for Schrödinger operator: some upper bounds |
| title_sort |
on the eigenvalue counting function for schrödinger operator: some upper bounds |
| publisher |
Sapienza Università Editrice |
| series |
Rendiconti di Matematica e delle Sue Applicazioni |
| issn |
1120-7183 2532-3350 |
| publishDate |
2018-01-01 |
| description |
The aim of this work is to provide an upper bound on the eigenvalues counting function N(Rn, −∆+V, e) of a Schr¨odinger operator −∆+V on R^n corresponding to a potential V ∈ L^(n/2 +ε) (Rn, dx), in terms of the sum of the eigenvalues counting function of the Dirichlet integral D with Dirichlet boundary conditions on the subpotential domain {V < e}, endowed with weighted Lebesgue measure (V − e)− · dx and the eigenvalues counting function of the absorption-to-reflection operator on the equipotential surface {V = e}. |
| topic |
Schr¨odinger operators eigenvalues counting function Dirichlet-to-Neumann operator |
| url |
http://www1.mat.uniroma1.it/ricerca/rendiconti/39_2_(2018)_257-276.html |
| work_keys_str_mv |
AT fabiocipriani ontheeigenvaluecountingfunctionforschrodingeroperatorsomeupperbounds |
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1724753648512139264 |