# On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.

Collectanea Mathematica (2006)

- Volume: 57, Issue: 3, page 279-293
- ISSN: 0010-0757

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topYakubovich, Semyon B.. "On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.." Collectanea Mathematica 57.3 (2006): 279-293. <http://eudml.org/doc/41775>.

@article{Yakubovich2006,

abstract = {We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = 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.},

author = {Yakubovich, Semyon B.},

journal = {Collectanea Mathematica},

keywords = {Transformadas integrales; Distribuciones; Funciones de Bessel; Ecuaciones diferenciales elípticas; Problema de Dirichlet; distributions; Kantorovich-Lebedev transform; modified Bessel functions; Dirichlet problem},

language = {eng},

number = {3},

pages = {279-293},

title = {On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.},

url = {http://eudml.org/doc/41775},

volume = {57},

year = {2006},

}

TY - JOUR

AU - Yakubovich, Semyon B.

TI - On a testing-function space for distributions associated with the Kontorovich-Lebedev transform.

JO - Collectanea Mathematica

PY - 2006

VL - 57

IS - 3

SP - 279

EP - 293

AB - We construct a testing function space, which is equipped with the topology that is generated by Lν,p - multinorm of the differential operatorAx = x2 - x d/dx [x d/dx],and its k-th iterates Akx, where k = 0, 1, ... , and A0xφ = 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.

LA - eng

KW - Transformadas integrales; Distribuciones; Funciones de Bessel; Ecuaciones diferenciales elípticas; Problema de Dirichlet; distributions; Kantorovich-Lebedev transform; modified Bessel functions; Dirichlet problem

UR - http://eudml.org/doc/41775

ER -

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