English

Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation

Functional Analysis 2025-09-30 v1

Abstract

In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation theory. The setting in complete semi-vector spaces does not requite additional assumptions but is intrinsically built into the frame work. For the purposes of this paper, fractal interpolation in the complete semi-vector spaces C+C^+ and Lp+L_p^+ is considered.

Keywords

Cite

@article{arxiv.2509.24512,
  title  = {Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation},
  author = {Peter R. Massopust},
  journal= {arXiv preprint arXiv:2509.24512},
  year   = {2025}
}