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PreprintCC BY 4.0arXiv

The differentiation and integration operator on weighted spaces of analytic functions in the weight sequence setting

  • Gerhard Schindl
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Abstract

We investigate the differentiation and integration operator defined on resp. between weighted spaces of analytic functions in the special situation when the weight is given in terms of a weight sequence. More precisely, in this case the weight is defined via the associated weight function which is a crucial object in the ultradifferentiable setting and the information can be then expressed purely in terms of the underlying weight sequence. Due to the additional structure this setting is exploited in order to construct (counter-)examples, to compare conditions on weights in the different weighted frameworks, and to study and to understand in a more precise qualitative way required and admissible growth restrictions on the weights.

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Cite

BibTeXRIS
BibTeX
@misc{schindl2026differentiation,
  title = {{The differentiation and integration operator on weighted spaces of analytic functions in the weight sequence setting}},
  author = {Gerhard Schindl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11902},
  eprint = {2610.11902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11902},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The differentiation and integration operator on weighted spaces of analytic functions in the weight sequence setting
AU  - Gerhard Schindl
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11902
UR  - https://arxiv.org/abs/2610.11902
AB  - We investigate the differentiation and integration operator defined on resp. between weighted spaces of analytic functions in the special situation when the weight is given in terms of a weight sequence. More precisely, in this case the weight is defined via the associated weight function which is a crucial object in the ultradifferentiable setting and the information can be then expressed purely in terms of the underlying weight sequence. Due to the additional structure this setting is exploited in order to construct (counter-)examples, to compare conditions on weights in the different weighted frameworks, and to study and to understand in a more precise qualitative way required and admissible growth restrictions on the weights.
ER  -