| Title:
|
The $\Cal L_\nu^{(\rho )}$-transformation on McBride's spaces of generalized functions (English) |
| Author:
|
Cruz-Báez, D. I. |
| Author:
|
Rodríguez, J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
445-452 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Krätzel integral transformation |
| Keyword:
|
$L_p$-spaces |
| Keyword:
|
distributions |
| MSC:
|
44A10 |
| MSC:
|
44A15 |
| MSC:
|
46F12 |
| idZBL:
|
Zbl 0971.44002 |
| idMR:
|
MR1666833 |
| . |
| Date available:
|
2009-01-08T18:45:10Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119023 |
| . |
| Reference:
|
[1] 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. Zbl 0844.44002, MR 1104376 |
| Reference:
|
[2] Barrios J.A., Betancor J.J.: A Real Inversion Formula for the Krätzel's Generalized Laplace Transform.Extracta Mathematicae 6 (2) (1991), 55-57. |
| Reference:
|
[3] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.: Tables of Integral Transforms, Vol. II.McGraw-Hill, New York, 1954. Zbl 0058.34103, MR 0065685 |
| Reference:
|
[4] 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. |
| Reference:
|
[5] Krätzel E.: Eine verallgemeinerung der Laplace- und Meijer-transformation.Wiss. Z. Univ. Jena Math. Naturw. Reihe 5 (1965), 369-381. MR 0231142 |
| Reference:
|
[6] Krätzel E.: Die faltung der L-transformation.Wiss. Z. Univ. Jena Math. Naturw. Reihe 5 (1965), 383-390. MR 0231143 |
| Reference:
|
[7] Krätzel E.: Integral transformations of Bessel-type.Proceeding of International Conference on Generalized Functions and Operational Calculus, Varna, 1975, pp.148-155. MR 0547343 |
| Reference:
|
[8] Krätzel E., Menzer H.: Verallgemeinerte Hankel-Funktionen.Pub. Math. Debrecen 18, fasc. 1-4 (1973), 139-148. MR 0310309 |
| Reference:
|
[9] McBride A.C.: Fractional Calculus and Integral Transforms of Generalized Functions.Res. Notes Math., 31, Pitman Press, San Francisco, London, Melbourne, 1979. Zbl 0423.46029, MR 0550881 |
| Reference:
|
[10] McBride A.C.: Fractional powers of a class ordinary differential operators.Proc. London Math. Soc., Ser. 3 45 (1982), 3 519-546. MR 0675420 |
| Reference:
|
[11] Rao G.L.N., Debnath L.: A generalized Meijer transformation.Int. J. Math. & Math. Sci. 8:2 (1985), 359-365. Zbl 0597.46036, MR 0797835 |
| Reference:
|
[12] Zemanian A.H.: A distributional $K$ transformation.Siam J. Appl. Math. 14 6 (1966), 1350-1365. |
| Reference:
|
[13] Zemanian A.H: Generalized Integral Transformation.Interscience Publisher, New York, 1968. MR 0423007 |
| . |
