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