Stable Harmonic Analysis and Stable Transfer
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916726104391680 |
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| author | Sunohara, Matthew |
| author_facet | Sunohara, Matthew |
| contents | Langlands posed the question of whether a local functorial transfer map of stable tempered characters can be interpolated by the transpose of a linear operator between spaces of stable orbital integrals of test functions. These so-called stable transfer operators are intended to serve as the main local ingredient in Beyond Endoscopy, his proposed strategy for proving the Principle of Functoriality. Working over a local field of characteristic zero and assuming a hypothesis on the local Langlands correspondence for p-adic groups, we prove the existence of continuous stable transfer operators between spaces of stable orbital integrals of Harish-Chandra Schwartz functions, test functions, and K-finite test functions. This is achieved via stable Paley--Wiener theorems for each of the three types of function spaces. The stable Paley--Wiener theorem for Harish-Chandra Schwartz functions is new and includes the result that stable tempered characters span a weak-* dense subspace of the space of stable tempered distributions, a result previously unknown for p-adic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable Harmonic Analysis and Stable Transfer Sunohara, Matthew Number Theory Representation Theory 22E50 (Primary) 22E30, 22E35 (Secondary) Langlands posed the question of whether a local functorial transfer map of stable tempered characters can be interpolated by the transpose of a linear operator between spaces of stable orbital integrals of test functions. These so-called stable transfer operators are intended to serve as the main local ingredient in Beyond Endoscopy, his proposed strategy for proving the Principle of Functoriality. Working over a local field of characteristic zero and assuming a hypothesis on the local Langlands correspondence for p-adic groups, we prove the existence of continuous stable transfer operators between spaces of stable orbital integrals of Harish-Chandra Schwartz functions, test functions, and K-finite test functions. This is achieved via stable Paley--Wiener theorems for each of the three types of function spaces. The stable Paley--Wiener theorem for Harish-Chandra Schwartz functions is new and includes the result that stable tempered characters span a weak-* dense subspace of the space of stable tempered distributions, a result previously unknown for p-adic groups. |
| title | Stable Harmonic Analysis and Stable Transfer |
| topic | Number Theory Representation Theory 22E50 (Primary) 22E30, 22E35 (Secondary) |
| url | https://arxiv.org/abs/2505.04910 |