The $\Cal L_\nu^{(\rho )}$-transformation on McBride's spaces of generalized functions
Cruz-Báez, Domingo Israel ; Rodríguez, Josemar
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 445-452 / Harvested from Czech Digital Mathematics Library
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An integral transform denoted by ${\Cal L}_{\nu }^{(\rho )}$ that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.

Publié le : 1998-01-01
Classification:  44A10,  44A15,  46F12 
@article{119023,
     author = {Domingo Israel Cruz-B\'aez and Josemar Rodr\'\i guez},
     title = {The $\Cal L\_\nu^{(\rho )}$-transformation on McBride's spaces of generalized functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {445-452},
     zbl = {0971.44002},
     mrnumber = {1666833},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119023}
}

Cruz-Báez, Domingo Israel; Rodríguez, Josemar. The $\Cal L_\nu^{(\rho )}$-transformation on McBride's spaces of generalized functions. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 445-452. http://gdmltest.u-ga.fr/item/119023/

Barrios J.A.; Betancor J.J. On a generalization of Laplace transform due to E. Krätzel, J. Inst. Math. & Comp. Sci. (Math. Ser.) 3 (4) (1990), 273-291. (1990) | MR 1104376 | Zbl 0844.44002

Barrios J.A.; Betancor J.J. A Real Inversion Formula for the Krätzel's Generalized Laplace Transform, Extracta Mathematicae 6 (2) (1991), 55-57. (1991)

Erdelyi A.; Magnus W.; Oberhettinger F.; Tricomi F. Tables of Integral Transforms, Vol. II, McGraw-Hill, New York, 1954. | MR 0065685 | Zbl 0058.34103

Kilbas A.A.; Bonilla B.; Rivero M.; Rodríguez J.; Trujillo J. Bessel type function and Bessel type integral transform on spaces ${\Cal F}_{p,\mu }$ and ${\Cal F}_{p,\mu }^{^{\prime }}$, to appear.

Krätzel E. Eine verallgemeinerung der Laplace- und Meijer-transformation, Wiss. Z. Univ. Jena Math. Naturw. Reihe 5 (1965), 369-381. (1965) | MR 0231142

Krätzel E. Die faltung der L-transformation, Wiss. Z. Univ. Jena Math. Naturw. Reihe 5 (1965), 383-390. (1965) | MR 0231143

Krätzel E. Integral transformations of Bessel-type, Proceeding of International Conference on Generalized Functions and Operational Calculus, Varna, 1975, pp.148-155. | MR 0547343

Krätzel E.; Menzer H. Verallgemeinerte Hankel-Funktionen, Pub. Math. Debrecen 18, fasc. 1-4 (1973), 139-148. (1973) | MR 0310309

Mcbride A.C. Fractional Calculus and Integral Transforms of Generalized Functions, Res. Notes Math., 31, Pitman Press, San Francisco, London, Melbourne, 1979. | MR 0550881 | Zbl 0423.46029

Mcbride A.C. Fractional powers of a class ordinary differential operators, Proc. London Math. Soc., Ser. 3 45 (1982), 3 519-546. (1982) | MR 0675420

Rao G.L.N.; Debnath L. A generalized Meijer transformation, Int. J. Math. & Math. Sci. 8:2 (1985), 359-365. (1985) | MR 0797835 | Zbl 0597.46036

Zemanian A.H. A distributional $K$ transformation, Siam J. Appl. Math. 14 6 (1966), 1350-1365. (1966)

Zemanian A.H Generalized Integral Transformation, Interscience Publisher, New York, 1968. | MR 0423007