Almost everywhere convergence of a wavelet-type Malmquist-Takenaka series
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911339409047552 |
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| author | Mnatsakanyan, Gevorg |
| author_facet | Mnatsakanyan, Gevorg |
| contents | The Malmquist-Takenaka (MT) system is a complete orthonormal system in $H^2(\mathbf{T})$ generated by an arbitrary sequence of points $a_n$ in the unit disk with $\sum_n (1-|a_n|) = \infty$. The point $a_n$ is responsible for multiplying the $n$th and subsequent terms of the system by a Möbius transform taking $a_n$ to $0$. One can recover the classical trigonometric system, its perturbations or conformal transformations, as particular examples of the MT system. However, many interesting choices of the sequence $a_n$, the MT system is less understood. In this paper, we consider a wavelet-type MT system and prove its almost everywhere convergence in $H^2(\mathbf{T})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost everywhere convergence of a wavelet-type Malmquist-Takenaka series Mnatsakanyan, Gevorg Classical Analysis and ODEs The Malmquist-Takenaka (MT) system is a complete orthonormal system in $H^2(\mathbf{T})$ generated by an arbitrary sequence of points $a_n$ in the unit disk with $\sum_n (1-|a_n|) = \infty$. The point $a_n$ is responsible for multiplying the $n$th and subsequent terms of the system by a Möbius transform taking $a_n$ to $0$. One can recover the classical trigonometric system, its perturbations or conformal transformations, as particular examples of the MT system. However, many interesting choices of the sequence $a_n$, the MT system is less understood. In this paper, we consider a wavelet-type MT system and prove its almost everywhere convergence in $H^2(\mathbf{T})$. |
| title | Almost everywhere convergence of a wavelet-type Malmquist-Takenaka series |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2404.13296 |