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## Banach Center Publications

2000 | 53 | 1 | 155-165
Tytuł artykułu

### Hankel type integral transforms connected with the hyper-Bessel differential operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we give a solution of a problem posed by the second author in her book, namely, to find symmetrical integral transforms of Fourier type, generalizing the cos-Fourier (sin-Fourier) transform and the Hankel transform, and suitable for dealing with the hyper-Bessel differential operators of order m>1 $B:= x^{-β} ∏_{j=1}^{m} (x(d/dx) + βγ_{j})$, β>0, $γ_{j} ∈ R$, j=1,...,m. We obtain such integral transforms corresponding to hyper-Bessel operators of even order 2m and belonging to the class of the Mellin convolution type transforms with the Meijer G-function as kernels. Inversion formulas and some operational relations for these transforms are found.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
155-165
Opis fizyczny
Daty
wydano
2000
Twórcy
autor
• Department of Mathematics and Computer Science, Free University of Berlin, Arnimallee 2-6, D-14195 Berlin, Germany
• Institute of Mathematics, Bulgarian Academy of Sciences, Sofia 1090, Bulgaria
Bibliografia
• [1] B. L. J. Braaksma and A. Schuitman, Some classes of Watson transforms and related integral equations for generalized functions, SIAM J. Math. Anal. 7 (1976), 771-798.
• [2] I. Dimovski, A transform approach to operational calculus for the general Bessel-type differential operator, C.R. Acad. Bulg. Sci. 27 (1974), 155-158.
• [3] C. Fox, The $G$- and $H$-functions as symmetrical Fourier kernels, Trans. Amer. Math. Soc. 98 (1961), 395-429.
• [4] V. S. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Res. Notes in Math. Ser. 301, Longman Sci. & Technical, Harlow, 1994.
• [5] Yu. F. Luchko and S. B. Yakubovich, Convolutions for the generalized fractional integration operators, in: Proc. Intern. Conf. 'Complex Analysis and Appl.' (Varna, 1991), Sofia, 1993, 199-211.
• [6] O. I. Marichev, Handbook of Integral Transforms of Higher Transcendental Functions. Theory and Algorithmic Tables, Ellis Horwood, Chichester, 1983.
• [7] N. Obrechkoff, On some integral representations of real functions on the real semi-axis, Izvestija Mat. Institut (BAS-Sofia) 3, No 1 (1958), 3-28 (in Bulgarian); Engl. transl. in: East J. on Approximations 3, No 1 (1997), 89-110.
• [8] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and Series. Vol. 3: More Special Functions, Gordon and Breach, New York - London - Paris - Montreux - Tokyo, 1989.
• [9] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, London - New York, 1993.
• [10] E. C. Titchmarsh, Introduction to Theory of Fourier Integrals, Oxford Univ. Press, Oxford, 1937.
• [11] K. T. Vu, Integral Transforms and Their Composition Structure, Dr.Sc. thesis, Minsk, 1987 (in Russian).
• [12] K. T. Vu, O. I. Marichev and S. B. Yakubovich, Composition structure of integral transformations, J. Soviet Math. 33 (1986), 166-169.
• [13] S. B. Yakubovich and Yu. F. Luchko, Hypergeometric Approach to Integral Transforms and Convolutions, Mathematics and Its Applications 287, Kluwer Acad. Publ., Dordrecht - Boston - London, 1994.
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Bibliografia
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