A distribution associated with the Kontorovich-Lebedev transform

• Autorzy: Yakubovich S.B.
• Języki publikacji: EN

Abstrakty

EN

We show that in a sense of distributions [formula], where δ is the Dirac distribution, τ, x ∈ R and Kν(x) is the modified Bessel function. The convergence is in E'(R) for any even varphi(x) ∈ E(R) being a restriction to R of a function varphi(z) analytic in a horizontal open strip Ga = {z ∈ C: |Im z| < a, a > 0} and continuous in the strip closure. Moreover, it satisfles the condition [formula], |Re z| → ∞, α > 1 uniformly in ‾Ga. The result is applied to prove the representation theorem for the inverse Kontorovich-Lebedev transformation on distributions.

Słowa kluczowe

EN

Kontorovich-Lebedev transform; distributions; modified Bessel functions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 1
• Strony: 161--172
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Yakubovich S.B.

• University of Porto, Faculty of Sciences, Department of Pure Mathematics, Campo Alegre st., 687, 4169-007 Porto, Portugal,

Bibliografia

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