Restriction Theorem and Strichartz estimate for orthonormal functions associated with the Special Hermite Operator
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| Format: | Preprint |
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2025
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| _version_ | 1866914166496821248 |
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| author | Ghosh, Sunit Swain, Jitendriya |
| author_facet | Ghosh, Sunit Swain, Jitendriya |
| contents | Let $\mathcal{L}$ be the special Hermite operator on $\mathbb{C}^n$. As a continuation of the recent results in \cite{SG}, we establish new Strichartz estimates for systems of orthonormal functions associated with general flows of the form $e^{-itϕ(\mathcal{L})}$, where $ ϕ: \mathbb{R}^{+} \to \mathbb{R} $ is a smooth function. Our approach relies on restriction estimates for the Fourier-special Hermite transform on the class of surfaces $\{(λ, μ, ν)\in \mathbb{R}\times\mathbb{N}_0^n\times\mathbb{N}_0^n : λ=ϕ(2|ν|+n)\}$. We also discuss the endpoint case of the orthonormal Strichartz estimate for the Schrödinger propagator $e^{-it\mathcal{L}}$. Furthermore, we generalize restriction estimates for the special Hermite spectral projections in the context of trace ideals (Schatten spaces). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_17230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restriction Theorem and Strichartz estimate for orthonormal functions associated with the Special Hermite Operator Ghosh, Sunit Swain, Jitendriya Functional Analysis Let $\mathcal{L}$ be the special Hermite operator on $\mathbb{C}^n$. As a continuation of the recent results in \cite{SG}, we establish new Strichartz estimates for systems of orthonormal functions associated with general flows of the form $e^{-itϕ(\mathcal{L})}$, where $ ϕ: \mathbb{R}^{+} \to \mathbb{R} $ is a smooth function. Our approach relies on restriction estimates for the Fourier-special Hermite transform on the class of surfaces $\{(λ, μ, ν)\in \mathbb{R}\times\mathbb{N}_0^n\times\mathbb{N}_0^n : λ=ϕ(2|ν|+n)\}$. We also discuss the endpoint case of the orthonormal Strichartz estimate for the Schrödinger propagator $e^{-it\mathcal{L}}$. Furthermore, we generalize restriction estimates for the special Hermite spectral projections in the context of trace ideals (Schatten spaces). |
| title | Restriction Theorem and Strichartz estimate for orthonormal functions associated with the Special Hermite Operator |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2511.17230 |