A Glazman–Povzner–Wienholtz theorem on graphs
| Autor: | Mark Malamud, Noema Nicolussi, Aleksey Kostenko |
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| Rok vydání: | 2022 |
| Předmět: |
General Mathematics
010102 general mathematics Mathematics::Analysis of PDEs FOS: Physical sciences Mathematical Physics (math-ph) Mathematics::Spectral Theory 16. Peace & justice 01 natural sciences Functional Analysis (math.FA) Mathematics - Spectral Theory Mathematics - Functional Analysis 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Nonlinear Sciences::Pattern Formation and Solitons Spectral Theory (math.SP) Mathematical Physics |
| Zdroj: | Advances in Mathematics. 395:108158 |
| ISSN: | 0001-8708 |
| Popis: | The Glazman-Povzner-Wienholtz theorem states that the completeness of a manifold, when combined with the semiboundedness of the Schr\"odinger operator $-\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its essential self-adjointness. Our aim is to extend this result to Schr\"odinger operators on graphs. We first obtain the corresponding theorem for Schr\"odinger operators on metric graphs, allowing in particular distributional potentials $q\in H^{-1}_{\rm loc}$. Moreover, we exploit recently discovered connections between Schr\"odinger operators on metric graphs and weighted graphs in order to prove a discrete version of the Glazman-Povzner-Wienholtz theorem. Comment: 24 pages; After submission we learned that the discrete version of the Glazman-Povzner-Wienholtz theorem (Theorem 6.1) was proved earlier by a different approach in arXiv:1301.1304 (see Theorem 2.16 there) |
| Databáze: | OpenAIRE |
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