English

Herglotz representation for operator-valued function on a set associated with test functions

Functional Analysis 2024-11-25 v1 Complex Variables

Abstract

The Herglotz representation theorem for holomorphic functions with non-negative real part is a fundamental result in the theory of holomorphic functions. In this paper, we reinterpret the Herglotz representation in the context of modern techniques, specifically realization formula. This reinterpretation is then extended to operator-valued functions on arbitrary sets, in association with a collection of test functions.

Keywords

Cite

@article{arxiv.2411.14455,
  title  = {Herglotz representation for operator-valued function on a set associated with test functions},
  author = {Mainak Bhowmik and Poornendu Kumar},
  journal= {arXiv preprint arXiv:2411.14455},
  year   = {2024}
}

Comments

To appear in Proc. Amer. Math. Soc. arXiv admin note: text overlap with arXiv:2311.15568

R2 v1 2026-06-28T20:08:16.352Z