Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
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
Czasopismo
Rocznik
Tom
Strony
161--172
Opis fizyczny
Bibliogr. 8 poz.
Twórcy
autor
- University of Porto, Faculty of Sciences, Department of Pure Mathematics, Campo Alegre st., 687, 4169-007 Porto, Portugal, syakubov@fc.up.pt
Bibliografia
- [1] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.G., Higher Transcendental Functions, Vol. II, McGraw-Hill, New York, London and Toronto, 1953.
- [2] Forristall G. Z., Ingram J.D., Evaluation of distributions useful in Kontorovich-Lebedev transform theory, SIAM J: Math. Anal. 3 (1972), 561-566.
- [3] Prudnikov A. P., Brychkov Yu. A., Marichev O.I., Integrals and Series, Special Functions, Gordon and Breach, New York, 1986.
- [4] Sneddon I.N., The Use of Integral Transforms, McGraw-Hill, New York, 1972.
- [5] Yakubovich S.B., Fisher B., On the theory of the Kontorovich-Lebedev transformation on distributions, Proc. of the Amer. Math. Soc, 122 (1994) 3, 773-777.
- [6] Yakubovich S.B., Luchko Yu. F., The Hypergeometric Approach to Integral Transforms and Convolutions, (Kluwers Ser. Math. and Appl.: Vol. 287), Dordrecht, Boston, London, 1994.
- [7] Yakubovich S.B., Index Transforms, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1996.
- [8] Zemanian A.H., The Kontorovich-Lebedev transformation on distributions of compact support and its inversion, Math. Proc. Cambridge Philos. Soc. 77 (1975), 139-143.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0006-0012