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PreprintCC BY 4.0arXiv

Generalized functions in a Non-Archimedean field

  • Vieri Benci
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Abstract

Ultrafunctions are generalized functions defined on a non-Archimedean field extending R. They provide a framework for treating problems that fall outside the classical theory of distributions. In this paper we introduce an improved notion of ultrafunctions which refines the previous constructions. This new approach allows a more flexible functional framework than the one used in other papers and yields a more flexible functional setting. In particular, this approach allows us to prove the existence of ultrafunction solutions for several classes of ill-posed evolution problems arising in partial differential equations.

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Cite

BibTeXRIS
BibTeX
@misc{benci2026generalized,
  title = {{Generalized functions in a Non-Archimedean field}},
  author = {Vieri Benci},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07279},
  eprint = {2609.07279},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07279},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized functions in a Non-Archimedean field
AU  - Vieri Benci
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07279
UR  - https://arxiv.org/abs/2609.07279
AB  - Ultrafunctions are generalized functions defined on a non-Archimedean field extending R. They provide a framework for treating problems that fall outside the classical theory of distributions. In this paper we introduce an improved notion of ultrafunctions which refines the previous constructions. This new approach allows a more flexible functional framework than the one used in other papers and yields a more flexible functional setting. In particular, this approach allows us to prove the existence of ultrafunction solutions for several classes of ill-posed evolution problems arising in partial differential equations.
ER  -