The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929269940158464 |
|---|---|
| author | Shemyakov, Vladimir |
| author_facet | Shemyakov, Vladimir |
| contents | In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitive considerations may suggest that the function still assumes a specific value at infinity in a certain sense. In Nevanlinna theory, all objects are studied on average, i.e., their integrals, hence the integral interpretation of the concept of convergence to a limit is beneficial for the theory of meromorphic functions. This is precisely the focus of this work, applied to sums of Cauchy kernels and their derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04152 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity Shemyakov, Vladimir Complex Variables In analysis, it's often useful to know the value of a function at infinity, this operation possesses pleasant properties. However, even when the limit does not exist, some intuitive considerations may suggest that the function still assumes a specific value at infinity in a certain sense. In Nevanlinna theory, all objects are studied on average, i.e., their integrals, hence the integral interpretation of the concept of convergence to a limit is beneficial for the theory of meromorphic functions. This is precisely the focus of this work, applied to sums of Cauchy kernels and their derivatives. |
| title | The infinitesimal behavior of the sum of Cauchy kernels and its derivative at infinity |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2403.04152 |