×

Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator. (English) Zbl 1266.46031

The authors investigate the fractional Fourier transform of tempered distributions. The main result of the paper gives the boundedness of generalized pseudo-differential operators (defined in terms of the fractional Fourier transform) when acting on generalized Sobolev spaces.

MSC:

46F12 Integral transforms in distribution spaces
47G30 Pseudodifferential operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Almeida L.B.: The fractional Fourier transform and time–frequency representations. IEEE Trans. Signal Process. 42(11), 3084–3091 (1994) · doi:10.1109/78.330368
[2] Bhosale B.N., Chaudhary M.S.: Fractional Fourier transform of distributions of compact support. Bull. Cal. Math. Soc. 94(5), 349–358 (2002) · Zbl 1030.46048
[3] Pathak R.S.: A Course in Distribution Theory and Applications. Narosa Publishing House, New Delhi (2009) · Zbl 1173.42328
[4] Prasad A., Kumar M.: Product of two generalized pseudo-differential operators involving fractional Fourier transform. J. Pseudo Differ. Oper. Appl. 2(3), 355–365 (2011) · Zbl 1268.47062 · doi:10.1007/s11868-011-0034-5
[5] Zaidman, S.: Distributions and Pseudo-differential Operators. Longman, Essex., England (1991) · Zbl 0743.46029
[6] Zayed A.I.: Fractional Fourier transform of generalized functions. Integr. Transform. Spec. Funct. 7(3–4), 299–312 (1998) · Zbl 0941.46021 · doi:10.1080/10652469808819206
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.