Certain fundamental properties of generalized natural transform in generalized spaces

被引:5
作者
Al-Omari, Shrideh Khalaf [1 ]
Araci, Serkan [2 ]
机构
[1] Al Balqa Appl Univ, Fac Engn Technol, Dept Phys & Basic Sci, Amman 11134, Jordan
[2] Hasan Kalyoncu Univ, Fac Econ Adm & Social Sci, Dept Econ, TR-27410 Gaziantep, Turkey
关键词
Natural transform; Generalized natural transform; Boehmian; UltraBoehmian; Sumudu transform; Laplace transform;
D O I
10.1186/s13662-021-03328-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386-1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.
引用
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页数:11
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