arXiv subjects

Samuel A. Hokamp

Publications and source records attributed to Samuel A. Hokamp.

6 recordsLinked to original sources

arXiv2025

Properties of reproducing kernel Hilbert spaces of a group action

In this paper, we investigate properties of a reproducing kernel Hilbert space of a group action. In particular, we introduce an equivalence relation on a compact Hausdorff space $X$, and consequently establish three equivalent definitions for when two elements are related. We also see how the equivalence classes of $X$ correspond to subgroups of the group acting transitively on $X$, which we aptly refer to as relation stabilizers.

math.FA↗

arXiv2023

A Class of Homeomorphisms on Homogeneous Spaces of a Group Action

We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a locally convex topological vector space which is also convex must necessarily be trivial, ie. a singleton set. Additionally, this class of homeomorphisms allows us to relate the induced group action on the space of continuous functions to the action on the homogeneous space.

math.FA↗

arXiv2022

Spaces of Continuous and Measurable Functions Invariant under a Group Action

In this paper we characterize spaces of continuous and $L^p$-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work generalizes Nagel and Rudin's 1976 results concerning unitarily and Möbius invariant spaces of continuous and measurable functions defined on the unit sphere in $\mathbb{C}^n$.

math.FA↗

arXiv2022

Spaces of Bounded Measurable Functions Invariant Under a Group Action

In this paper we characterize spaces of $L^\infty$-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work generalizes the author's 2021 results concerning the specific case of unitarily and Möbius invariant spaces of $L^\infty$-functions defined on the unit sphere in $\mathbb{C}^n$.

math.FA↗

arXiv2021

Certain Invariant Spaces of Bounded Measurable Functions on a Sphere

In their 1976 paper, Nagel and Rudin characterize the closed unitarily and Möbius invariant spaces of continuous and $L^p$-functions on a sphere, for $1\leq p<\infty$. In this paper we provide an analogous characterization for the weak*-closed unitarily and Möbius invariant spaces of $L^\infty$-functions on a sphere. We also investigate the weak*-closed unitarily and Möbius invariant algebras of $L^\infty$-functions on a sphere.

math.FA↗

arXiv2019

Deformation Theories Controlled by Hochschild Cohomologies

We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the $d$-sphere for any $d\geq1$, we also investigate a deformation theory corresponding to the tertiary Hochschild cohomology, which naturally reduces to those studied for the secondary and usual Hochschild cohomologies under certain conditions.

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