Certain fundamental properties of generalized natural transform in generalized spaces
Abstract 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 an...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2021-03-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03328-6 |
| _version_ | 1818615487519522816 |
|---|---|
| author | Shrideh Khalaf Al-Omari Serkan Araci |
| author_facet | Shrideh Khalaf Al-Omari Serkan Araci |
| author_sort | Shrideh Khalaf Al-Omari |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-12-16T16:34:41Z |
| format | Article |
| id | doaj.art-9cb061eaffab488cb913903ea701e6c6 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-16T16:34:41Z |
| publishDate | 2021-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-9cb061eaffab488cb913903ea701e6c62022-12-21T22:24:30ZengSpringerOpenAdvances in Difference Equations1687-18472021-03-012021111110.1186/s13662-021-03328-6Certain fundamental properties of generalized natural transform in generalized spacesShrideh Khalaf Al-Omari0Serkan Araci1Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied UniversityDepartment of Economics Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu UniversityAbstract 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.https://doi.org/10.1186/s13662-021-03328-6Natural transformGeneralized natural transformBoehmianUltraBoehmianSumudu transformLaplace transform |
| spellingShingle | Shrideh Khalaf Al-Omari Serkan Araci Certain fundamental properties of generalized natural transform in generalized spaces Advances in Difference Equations Natural transform Generalized natural transform Boehmian UltraBoehmian Sumudu transform Laplace transform |
| title | Certain fundamental properties of generalized natural transform in generalized spaces |
| title_full | Certain fundamental properties of generalized natural transform in generalized spaces |
| title_fullStr | Certain fundamental properties of generalized natural transform in generalized spaces |
| title_full_unstemmed | Certain fundamental properties of generalized natural transform in generalized spaces |
| title_short | Certain fundamental properties of generalized natural transform in generalized spaces |
| title_sort | certain fundamental properties of generalized natural transform in generalized spaces |
| topic | Natural transform Generalized natural transform Boehmian UltraBoehmian Sumudu transform Laplace transform |
| url | https://doi.org/10.1186/s13662-021-03328-6 |
| work_keys_str_mv | AT shridehkhalafalomari certainfundamentalpropertiesofgeneralizednaturaltransformingeneralizedspaces AT serkanaraci certainfundamentalpropertiesofgeneralizednaturaltransformingeneralizedspaces |