About the Laplace transform on ${{L}^{1}}\left( \mathbb{R^+} \right)$

Nargiza Boboyarova^a, Jonibek Abdullayev<sup>b

a</sup> Urgench technological university RANCH, house 26 Khanka street, Urgench city, 220100, Uzbekistan
^b Urgench State University, 14, Kh.Alimdjan str, Urgench city, 220100, Uzbekistan

Abstract: In the paper some preliminaries are stated, including the basic properties of $\mathscr{L}L^1(\mathbb{R}^+)$. As the appropriate conditions for $g\in \mathscr{L}L^1(\mathbb{R}^+),$ we attempted to take those ones formulated in the paper.

Keywords and phrases: laplace transformation, space $L^1(\mathbb R^+)$, Banach spaces.

MSC: 44A10, 46E15, 97I80

Received: 19.01.2024

Language: English

DOI: 10.56415/basm.y2025.i1.p43