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

Yakubovich, 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 -