Distributional Watson transforms

A. Dijksma; H.S.V.  de Snoo

doi:10.1137/0505084

Distributional Watson transforms

A. Dijksma, H.S.V. de Snoo

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Abstract

For all Watson transforms W in L2(R+) a triple of Hilbert space LG ⊂ L2(R+) ⊂ L'G is constructed such that W may be extended to L'G. These results allow the construction of a triple L ⊂ L2(R+) ⊂ L', where L is a Gelfand-Fréchet space. This leads to a theory of distributional Watson transforms.

Original language	English
Pages (from-to)	888-892
Number of pages	5
Journal	Siam journal on mathematical analysis
Volume	5
Issue number	6
DOIs	https://doi.org/10.1137/0505084
Publication status	Published - 1974

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title = "Distributional Watson transforms",

abstract = "For all Watson transforms W in L2(R+) a triple of Hilbert space LG ⊂ L2(R+) ⊂ L'G is constructed such that W may be extended to L'G. These results allow the construction of a triple L ⊂ L2(R+) ⊂ L', where L is a Gelfand-Fr{\'e}chet space. This leads to a theory of distributional Watson transforms.",

author = "A. Dijksma and {de Snoo}, H.S.V.",

note = "Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)",

year = "1974",

doi = "10.1137/0505084",

language = "English",

volume = "5",

pages = "888--892",

journal = "Siam journal on mathematical analysis",

issn = "0036-1410",

number = "6",

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T1 - Distributional Watson transforms

AU - Dijksma, A.

AU - de Snoo, H.S.V.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 1974

Y1 - 1974

N2 - For all Watson transforms W in L2(R+) a triple of Hilbert space LG ⊂ L2(R+) ⊂ L'G is constructed such that W may be extended to L'G. These results allow the construction of a triple L ⊂ L2(R+) ⊂ L', where L is a Gelfand-Fréchet space. This leads to a theory of distributional Watson transforms.

AB - For all Watson transforms W in L2(R+) a triple of Hilbert space LG ⊂ L2(R+) ⊂ L'G is constructed such that W may be extended to L'G. These results allow the construction of a triple L ⊂ L2(R+) ⊂ L', where L is a Gelfand-Fréchet space. This leads to a theory of distributional Watson transforms.

U2 - 10.1137/0505084

DO - 10.1137/0505084

M3 - Article

SN - 0036-1410

VL - 5

SP - 888

EP - 892

JO - Siam journal on mathematical analysis

JF - Siam journal on mathematical analysis

IS - 6

ER -