The Hankel transform of tempered Boehmians via the exchange property. (English) Zbl 1302.46029
The authors investigate the Hankel transform of tempered Boehmians. A localization principle for distributions in \(\mathcal{B}_{\mu}^{'}\) is given in Section 2. The proofs of the main results are given in Section 3, whereas in Section 4, algebraic properties and convergence in \(\chi_{\mu}\) are dealt with.
Remarks: In Ref.[19] [A. Singh et al., Int.J. Math.Anal., Ruse 4, No. 45–48, 2199–2210 (2010; Zbl 1250.46028)], the convolution of an integral transform is described in Eqn.(7), and using the relation between the two-dimensional Fourier transformation and the Hankel transform, tempered Boehmians are defined. Two theorems are proved for tempered Boehmians, and as the definition of Boehmians relies on convolution, these theorems are proved based on Eqn.(7) using the Hankel transform of order zero. The use of convolution is mandatory to define Boehmians.
Remarks: In Ref.[19] [A. Singh et al., Int.J. Math.Anal., Ruse 4, No. 45–48, 2199–2210 (2010; Zbl 1250.46028)], the convolution of an integral transform is described in Eqn.(7), and using the relation between the two-dimensional Fourier transformation and the Hankel transform, tempered Boehmians are defined. Two theorems are proved for tempered Boehmians, and as the definition of Boehmians relies on convolution, these theorems are proved based on Eqn.(7) using the Hankel transform of order zero. The use of convolution is mandatory to define Boehmians.
Reviewer: Abhishek Singh (Jodhpur)
MSC:
| 46F12 | Integral transforms in distribution spaces |
| 44A35 | Convolution as an integral transform |
| 46F99 | Distributions, generalized functions, distribution spaces |
Citations:
Zbl 1250.46028References:
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