A survey on the resolvent convergence
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917072703848448 |
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| author | Duran, Joaquim |
| author_facet | Duran, Joaquim |
| contents | This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of their spectra. We also explore the relations that these notions of convergence have with the so-called strong graph limit, $G$-convergence, and $Γ$-convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17687 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A survey on the resolvent convergence Duran, Joaquim Analysis of PDEs Spectral Theory 47A10 This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of their spectra. We also explore the relations that these notions of convergence have with the so-called strong graph limit, $G$-convergence, and $Γ$-convergence. |
| title | A survey on the resolvent convergence |
| topic | Analysis of PDEs Spectral Theory 47A10 |
| url | https://arxiv.org/abs/2509.17687 |