| 陈泳,桑元琦.Hardy空间上一类算子与函数方程的解[J].数学年刊A辑,2026,(1):1~10 |
| Hardy空间上一类算子与函数方程的解 |
| Solutions to a Class of Operator-Involved Functional Equations on Hardy Spaces |
| Received:January 15, 2026 Revised:March 02, 2026 |
| DOI：10.16205/j.cnki.cama.2026.0001 |
| 中文关键词: Hardy空间 Toeplitz算子 Hankel算子 |
| 英文关键词:Hardy space Toeplitz operatror Hankel operator |
| 基金项目:国家自然科学基金(No.12271134, No.12201508) |
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| 中文摘要: |
| 考虑在Hardy空间上解关于u的方程: u2+βu?2P(u?)为常数, u(0)=0, 其中β为常数, P为Riesz投影. 证明了解析多项式、再生核的有限线性组合不是方程的非零解; 得到了当β=0时, 方程在H∞(T)中无非零解, 在H2(T)中存在非零解; 当β≠0时, 内函数不是方程的解. |
| 英文摘要: |
| This paper studies solutions u on the Hardy space to the equation u2+βu?2P(u?) is a constant, u(0)=0, where β is a constant and P denotes the Riesz projection. The authors prove that neither analytic polynomials nor finite linear combinations of reproducing kernels can be nonzero solutions of the equation. They also find that when β=0, the equation has no nonzero solution in H∞(T), while it does admit nonzero solutions in H2(T). When β≠0, inner functions are not solutions of the equation. |
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