| Title:
|
The index ${}_2F_1$-transform of generalized functions (English) |
| Author:
|
Hayek, N. |
| Author:
|
González, B. J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
657-671 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the index transformation $$ F(\tau ) = \int_{0}^{\infty} f(t) {}_{2}F_{1}( \mu + \frac{1}{2} + i \tau , \mu + \frac{1}{2} - i \tau ; \mu + 1; -t ) t^{\alpha} \, dt $$ ${}_{2}F_{1}( \mu + \frac{1}{2} + i \tau , \mu + \frac{1}{2} - i \tau ; \mu + 1; -t ) $ being the Gauss hypergeometric function, is defined on certain space of generalized functions and its inversion formula established for distributions of compact support on ${\bold I} = (0, \infty )$. (English) |
| Keyword:
|
hypergeometric function |
| Keyword:
|
index integral transform |
| Keyword:
|
generalized functions |
| MSC:
|
33C90 |
| MSC:
|
44A15 |
| MSC:
|
44A20 |
| MSC:
|
46F12 |
| idZBL:
|
Zbl 0793.46019 |
| idMR:
|
MR1263795 |
| . |
| Date available:
|
2009-01-08T18:07:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118623 |
| . |
| Reference:
|
[1] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.: Higher Transcendental Functions.vol. I, McGraw-Hill Book Co. Inc., New York, 1953. Zbl 0064.06302 |
| Reference:
|
[2] Erdelyi A., Magnus W., Oberhettinger F., Tricomi F.: Tables of Integral Transforms.vol. II, McGraw-Hill Book Co. Inc., New York, 1954. Zbl 0184.33704, MR 0065685 |
| Reference:
|
[3] Glaeske H.N., Hess A.: On the Convolution Theorem of the Mehler-Fock-Transform for a Class of Generalized Functions (II).Math. Nachr. (1988), 119-129. Zbl 0649.46037, MR 0952467 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Hayek N., Negrin E.R., Gonzalez B.J.: Una clase de transformada índice relacionada con la de Olevskii.Actas XIV Jornadas Hispano-Lusas de Matemáticas (Puerto de la Cruz), vol. I, 1989, pp. 401-405. MR 1112907 |
| Reference:
|
[7] Lebedev N.N.: Sur une formule d'inversion.Dokl. Akad. Nauk. SSSR 52 (1946), 655-658. MR 0021144 |
| Reference:
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[8] Mendez J.M.: La transformación integral de Hankel-Clifford.Tesis, Secretariado de Publicaciones, Univ. La Laguna, Col. Monog. N. 8, 1981. |
| Reference:
|
[9] Olver F.W.J.: Asymptotics and special functions.Academic Press, New York, 1967. Zbl 0982.41018, MR 0435697 |
| Reference:
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[10] Robin L.: Fonctions Sphériques de Legendre et Fonctions Sphéroidales, Tome II.GauthierVillars, Paris, 1958. Zbl 0088.05102, MR 0101928 |
| Reference:
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[11] Schwartz L.: Théorie des distributions.Hermann & Cie., Paris, 1966. Zbl 0962.46025, MR 0209834 |
| Reference:
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[12] Van Der Pol B., Bremer H.: Operational Calculus.Cambridge University Press, New York, 1964. |
| Reference:
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[13] Vu Kim Tuan, Marichev O.I., Yakubovich S.B.: Composition structure of integral transformations.Sov. Math. Dokl. 33 (1986), 166-170. Zbl 0604.44003 |
| Reference:
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[14] Zemanian A.H.: Generalized integral transformations.Interscience Publishers, New York, 1968. Zbl 0643.46029, MR 0423007 |
| Reference:
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| . |
