On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.
Yakubovich, Semyon B.
Collectanea Mathematica, Tome 57 (2006), p. 279-293 / Harvested from Biblioteca Digital de Matemáticas
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We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operator

Ax = x2 - x d/dx [x d/dx],

and its k-th iterates Ak x, where k = 0, 1, ... , and A0 xφ = φ. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution of the Dirichlet problem for a wedge for the harmonic type equation in terms of the Kontorovich-Lebedev integral.

Publié le : 2006-01-01
DMLE-ID : 4263 
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     title = {On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.},
     journal = {Collectanea Mathematica},
     volume = {57},
     year = {2006},
     pages = {279-293},
     zbl = {1116.46028},
     mrnumber = {MR2264323},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41775}
}

Yakubovich, Semyon B. On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.. Collectanea Mathematica, Tome 57 (2006) pp. 279-293. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41775/