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On 1-regular ordinary differential operators

Grzegorz Łysik (2000)

Annales Polonici Mathematici

Solutions to singular linear ordinary differential equations with analytic coefficients are found in the form of Laplace type integrals.

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

Semyon B. Yakubovich (2006)

Collectanea Mathematica

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...

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