The index 2 F 1 -transform of generalized functions

N. Hayek; Benito J. González

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 4, page 657-671
  • ISSN: 0010-2628

Abstract

top
In this paper the index transformation F ( τ ) = ∫ 0 ∞ f ( t ) 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 1 ; - t ) t α d t 2 F 1 ( μ + 1 2 + i τ , μ + 1 2 - i τ ; μ + 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 𝐈 = ( 0 , ∞ ) .

How to cite

top

Hayek, N., and González, Benito J.. "The index ${}_2F_1$-transform of generalized functions." Commentationes Mathematicae Universitatis Carolinae 34.4 (1993): 657-671. <http://eudml.org/doc/247470>.

@article{Hayek1993,
abstract = {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 $\{\mathbf \{I\}\} = (0, \infty )$.},
author = {Hayek, N., González, Benito J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hypergeometric function; index integral transform; generalized functions; index integral transform; Gauss hypergeometric function; space of generalized functions; inversion formula; distributions of compact support},
language = {eng},
number = {4},
pages = {657-671},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The index $\{\}_2F_1$-transform of generalized functions},
url = {http://eudml.org/doc/247470},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Hayek, N.
AU - González, Benito J.
TI - The index ${}_2F_1$-transform of generalized functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 4
SP - 657
EP - 671
AB - 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 ${\mathbf {I}} = (0, \infty )$.
LA - eng
KW - hypergeometric function; index integral transform; generalized functions; index integral transform; Gauss hypergeometric function; space of generalized functions; inversion formula; distributions of compact support
UR - http://eudml.org/doc/247470
ER -

References

top
  1. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F., Higher Transcendental Functions, vol. I, McGraw-Hill Book Co. Inc., New York, 1953. Zbl0064.06302
  2. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F., Tables of Integral Transforms, vol. II, McGraw-Hill Book Co. Inc., New York, 1954. Zbl0184.33704MR0065685
  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. (1988) Zbl0649.46037MR0952467
  4. Hayek N., Estudio de la ecuación diferencial x y ' ' + ( ν + 1 ) y ' + y = 0 y de sus aplicaciones, Collect. Mat. XVII (1966-67), 57-174. (1966-67) MR0224876
  5. Hayek N., Sobre la transformación de Hankel, Actas de la VIII Reunión Anual de Matemáticos Espa noles, Madrid, 1968, pp. 47-60. MR0420164
  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. MR1112907
  7. Lebedev N.N., Sur une formule d'inversion, Dokl. Akad. Nauk. SSSR 52 (1946), 655-658. (1946) MR0021144
  8. Mendez J.M., La transformación integral de Hankel-Clifford, Tesis, Secretariado de Publicaciones, Univ. La Laguna, Col. Monog. N. 8, 1981. 
  9. Olver F.W.J., Asymptotics and special functions, Academic Press, New York, 1967. Zbl0982.41018MR0435697
  10. Robin L., Fonctions Sphériques de Legendre et Fonctions Sphéroidales, Tome II, GauthierVillars, Paris, 1958. Zbl0088.05102MR0101928
  11. Schwartz L., Théorie des distributions, Hermann & Cie., Paris, 1966. Zbl0962.46025MR0209834
  12. Van Der Pol B., Bremer H., Operational Calculus, Cambridge University Press, New York, 1964. 
  13. Vu Kim Tuan, Marichev O.I., Yakubovich S.B., Composition structure of integral transformations, Sov. Math. Dokl. 33 (1986), 166-170. (1986) Zbl0604.44003
  14. Zemanian A.H., Generalized integral transformations, Interscience Publishers, New York, 1968. Zbl0643.46029MR0423007
  15. Zemanian A.H., The Kantorovich-Lebedev transformation on distributions of compact support and its inversion, Math. Proc. Camb. Philos. Soc. 77 (1975), 139-143. (1975) MR0355489

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.