The fourier-bessel series representation of the pseudo-differential operator (−r−1D)v

Singh, O.P.; Pandey, J.N.

dc.contributor.author	Singh, O.P.
dc.contributor.author	Pandey, J.N.
dc.date.accessioned	2021-09-02T07:36:09Z
dc.date.available	2021-09-02T07:36:09Z
dc.date.issued	1992-08
dc.identifier.issn	00029939
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/1601
dc.description.abstract	For a certain Fréchet space F consisting of complex-valued C°° functions defined on / = (0, oo) and characterized by their asymptotic behaviour near the boundaries, we show that: (I) The pseudo-differential operator (-x~lD)" , v e R, D = d/dx , is an automorphism (in the topological sense) on F ; (II) (-x~lD)u is almost an inverse of the Hankel transform hv in the sense that hl/o(x-xD)v(<p) = hfj((p), VpeF, V¡/El; (III) (—x~lD)r has a Fourier-Bessel series representation on a subspace Fb C F and also on its dual F¿ .	en_US
dc.description.sponsorship	Proceedings of the American Mathematical Society	en_US
dc.language.iso	en	en_US
dc.relation.ispartofseries	Issue 4,;Volume 115,
dc.subject	Fourier-bessel series	en_US
dc.subject	Pseudo-differential order	en_US
dc.title	The fourier-bessel series representation of the pseudo-differential operator (−r−1D)v	en_US
dc.type	Article	en_US