Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911925547302912 |
|---|---|
| author | Duong, Giao Ky Frank, Rupert L. Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai |
| author_facet | Duong, Giao Ky Frank, Rupert L. Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai |
| contents | We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator $-Δ- (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm of $W$ which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16482 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator Duong, Giao Ky Frank, Rupert L. Le, Thi Minh Thao Nam, Phan Thành Nguyen, Phuoc-Tai Mathematical Physics Functional Analysis Spectral Theory We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator $-Δ- (d-2)^2/(4|x|^2) -W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted $L^{d/2}-$norm of $W$ which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian. |
| title | Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator |
| topic | Mathematical Physics Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2312.16482 |