Rigged Hilbert spaces and inductive limits
S.A. Pol'shin

TL;DR
This paper presents a simplified method for constructing a rigged Hilbert space using inductive limits of finite-dimensional subspaces, enhancing the understanding of the structure of nuclear spaces.
Contribution
It introduces a new approach to building rigged Hilbert spaces by leveraging inductive limits, simplifying previous complex constructions.
Findings
Constructed a nuclear space as an inductive limit of finite-dimensional subspaces.
Established the rigged Hilbert space structure with the constructed nuclear space.
Simplified the existing construction by Bellomonte and Trapani.
Abstract
We construct a nuclear space as an inductive limit of finite-dimensional subspaces of a Hilbert space in such a way that becomes a rigged Hilbert space, thus simplifying the construction by Bellomonte and Trapani.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Operator Algebra Research · Mathematical Analysis and Transform Methods
