Asymptotic expansions for spectral convergence of compact self-adjoint operators on general spectral subsets, with application to kernel Gram matrices
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910015178145792 |
|---|---|
| author | Bae, Eunseong Polonik, Wolfgang |
| author_facet | Bae, Eunseong Polonik, Wolfgang |
| contents | We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on eigenvalues indexed by a general subset, with minimal restrictions on their selection. The usefulness of the provided expansions is illustrated by an application to kernel Gram matrices, deriving concentration inequalities as well as weak convergence results, which, in contrast to existing literature, are primarily relying on assumptions on the kernel that are easy to check. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00999 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic expansions for spectral convergence of compact self-adjoint operators on general spectral subsets, with application to kernel Gram matrices Bae, Eunseong Polonik, Wolfgang Statistics Theory Spectral Theory We study the spectral convergence of compact, self-adjoint operators on a separable Hilbert space under operator norm perturbations, and derive asymptotic expansions for their eigenvalues and eigenprojections. Our analysis focuses on eigenvalues indexed by a general subset, with minimal restrictions on their selection. The usefulness of the provided expansions is illustrated by an application to kernel Gram matrices, deriving concentration inequalities as well as weak convergence results, which, in contrast to existing literature, are primarily relying on assumptions on the kernel that are easy to check. |
| title | Asymptotic expansions for spectral convergence of compact self-adjoint operators on general spectral subsets, with application to kernel Gram matrices |
| topic | Statistics Theory Spectral Theory |
| url | https://arxiv.org/abs/2602.00999 |