On the space of Laplace transformable distributions

Area of Science:

• Functional Analysis
• Distribution Theory

Background:

• The space of Laplace transformable distributions, denoted S'(Γ), is crucial in various areas of mathematical analysis.
• Understanding the topological properties of S'(Γ) is essential for advanced mathematical research.

Purpose of the Study:

• To establish that the space of Laplace transformable distributions S'(Γ) over a non-empty convex open set Γ ⊆ R^d is an ultrabornological (PLS)-space.
• To determine an explicit topological predual for S'(Γ).

Main Methods:

• Utilizing concepts from functional analysis and topological vector spaces.
• Applying techniques related to the theory of distributions and their transforms.

Main Results:

• The space S'(Γ) is proven to be an ultrabornological (PLS)-space.
• An explicit topological predual of S'(Γ) has been successfully determined.

Conclusions:

• The findings contribute to a deeper understanding of the structure and properties of Laplace transformable distributions.
• The identification of the topological predual offers new avenues for further investigation in functional analysis.