On fractional convolutions and distributions

References

• Namias V. The fractional order Fourier transform and its application to quantum mechanics. IMA J Appl Math. 1980;25:241–265. doi: 10.1093/imamat/25.3.241
   Web of Science ®Google Scholar
• McBride AC, Kerr FH. On Namias's fractional Fourier transforms. IMA J Appl Math. 1987;39:159–175. doi: 10.1093/imamat/39.2.159
   Web of Science ®Google Scholar
• Zayed AI. On the relationship between the Fourier and fractional Fourier transforms. IEEE Signal Process Lett. 1996;3:310–311. doi: 10.1109/97.544785
   Web of Science ®Google Scholar
• Almeida LB. The fractional Fourier transform and time-frequency representations. IEEE Trans Signal Process. 1994;42:3084–3091. doi: 10.1109/78.330368
   Web of Science ®Google Scholar
• Almeida LB. Product and convolution theorems for the fractional Fourier transform. IEEE Signal Process Lett. 1997;4:15–17. doi: 10.1109/97.551689
   Web of Science ®Google Scholar
• Pathak RS, Prasad A, Kumar M. Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator. J Pseudo-Differential Oper Appl. 2012;3:239–254. doi: 10.1007/s11868-012-0047-8
   Web of Science ®Google Scholar
• Prasad A, Kumar M. Product of two generalized pseudo-differential operators involving fractional Fourier transform. J Pseudo-Differential Oper Appl. 2011;2:355–365. doi: 10.1007/s11868-011-0034-5
   Web of Science ®Google Scholar
• Prasad A, Mahato A. The fractional wavelet transform on spaces of type S. Integral Transforms Spec Funct. 2012;23:237–249. doi: 10.1080/10652469.2011.571213
   Web of Science ®Google Scholar
• Prasad A, Manna S, Mahato A, Singh VK. The generalized continuous wavelet transform associated with the fractional Fourier transform. J Comput Appl Math. 2014;259:660–671. doi: 10.1016/j.cam.2013.04.016
   Web of Science ®Google Scholar
• Prasad A, Kumar M. Boundedness of Pseudo-differential operator associated with fractional Fourier transform. Proc Natl Acad Sci India Sect A: Phys Sci. 2014;84:549–554. doi: 10.1007/s40010-014-0163-3
   Web of Science ®Google Scholar
• Shi J, Zhang N, Liu X. A novel fractional wavelet transform and its applications. Sci China Inform Sci. 2012;55:1270–1279. doi: 10.1007/s11432-011-4320-x
   Web of Science ®Google Scholar
• Zayed AI. Fractional Fourier transform of generalized functions. Integral Transforms Spec Funct. 1998;7:299–312. doi: 10.1080/10652469808819206
   Web of Science ®Google Scholar
• Nhan NDV, Duc DT. Weighted Lp-norm inequalities in convolutions and their applications. J Math Inequal. 2008;2:45–55. doi: 10.7153/jmi-02-06
   Google Scholar
• Nhan NDV, Duc DT. Reverse weighted Lp-norm inequalities and their applications. J Math Inequal. 2008;2:57–73. doi: 10.7153/jmi-02-07
   Google Scholar
• Nhan NDV, Duc DT, Tuan VK. Weighted Lp-norm inequalities for various convolution type transformations and their applications. Armen J Math. 2008;1:1–18.
   Google Scholar
• Nhan NDV, Duc DT, Tuan VK. Reverse weighted Lp-norm inequalities for convolution type integrals. Armen J Math. 2009;2:77–93.
   Google Scholar
• Nhan NDV, Duc DT. Norm inequalities for Mellin convolutions and their applications. Complex Anal Oper Theory. 2013;7:1287–1297. doi: 10.1007/s11785-012-0224-z
   Web of Science ®Google Scholar
• Andersen KF. Weighted inequalities for iterated convolutions. Proc Amer Math Soc. 1999;127:2643–2651. doi: 10.1090/S0002-9939-99-05271-5
   Web of Science ®Google Scholar
• Castro LP, Saitoh S. New convolutions and norm inequalities. Math Inequal Appl. 2012;12:707–716.
   Google Scholar
• Saitoh S, Tuan VK, Yamamoto M. Reverse convolution inequalities and applications to inverse heat source problems. J Inequal Pure Appl Math. 2002;3 [Article 80].
   Google Scholar
• Saitoh S, Tuan VK, Yamamoto M. Convolution inequalities and applications. J Inequal Pure Appl Math. 2003;4 [Article 50].
   Google Scholar
• Jain P, Jain S. On Young type inequalities for generalized convolutions. Proc A Razmadze Math Inst. 2014;164:45–61.
   Google Scholar
• Kesavan S. Topics in functional analysis and its applications. New York: Wiley; 1989.
   Google Scholar