Polynomially oscillatory multipliers on Gelfand-Shilov spaces
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916534952132608 |
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| author | Junior, Alexandre Arias Wahlberg, Patrik |
| author_facet | Junior, Alexandre Arias Wahlberg, Patrik |
| contents | We study continuity of the multiplier operator $e^{i q}$ acting on Gelfand--Shilov spaces, where $q$ is a polynomial on $\mathbf R^d$ of degree at least two with real coefficients. In the parameter quadrant for the spaces we identify a wedge that depends on the polynomial degree for which the operator is continuous. We also show that in a large part of the complement region the operator is not continuous in dimension one. The results give information on well-posedness for linear evolution equations that generalize the Schrödinger equation for the free particle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomially oscillatory multipliers on Gelfand-Shilov spaces Junior, Alexandre Arias Wahlberg, Patrik Functional Analysis Analysis of PDEs 42B35, 35B65, 47D03, 46F05, 46E10 We study continuity of the multiplier operator $e^{i q}$ acting on Gelfand--Shilov spaces, where $q$ is a polynomial on $\mathbf R^d$ of degree at least two with real coefficients. In the parameter quadrant for the spaces we identify a wedge that depends on the polynomial degree for which the operator is continuous. We also show that in a large part of the complement region the operator is not continuous in dimension one. The results give information on well-posedness for linear evolution equations that generalize the Schrödinger equation for the free particle. |
| title | Polynomially oscillatory multipliers on Gelfand-Shilov spaces |
| topic | Functional Analysis Analysis of PDEs 42B35, 35B65, 47D03, 46F05, 46E10 |
| url | https://arxiv.org/abs/2412.13642 |