The ℒ ν ( ρ ) -transformation on McBride’s spaces of generalized functions

Domingo Israel Cruz-Báez; Josemar Rodríguez

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 3, page 445-452
  • ISSN: 0010-2628

Abstract

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An integral transform denoted by ℒ ν ( ρ ) 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.

How to cite

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Cruz-Báez, Domingo Israel, and Rodríguez, Josemar. "The $\mathcal {L}_\nu ^{(\rho )}$-transformation on McBride’s spaces of generalized functions." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 445-452. <http://eudml.org/doc/248244>.

@article{Cruz1998,
abstract = {An integral transform denoted by $\{\mathcal \{L\}\}_\{\nu \}^\{(\rho )\}$ 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.},
author = {Cruz-Báez, Domingo Israel, Rodríguez, Josemar},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Krätzel integral transformation; $L_p$-spaces; distributions; Krätzel transformation; McBride space; distribution; generalized Laplace transformation},
language = {eng},
number = {3},
pages = {445-452},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The $\mathcal \{L\}_\nu ^\{(\rho )\}$-transformation on McBride’s spaces of generalized functions},
url = {http://eudml.org/doc/248244},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Cruz-Báez, Domingo Israel
AU - Rodríguez, Josemar
TI - The $\mathcal {L}_\nu ^{(\rho )}$-transformation on McBride’s spaces of generalized functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 3
SP - 445
EP - 452
AB - An integral transform denoted by ${\mathcal {L}}_{\nu }^{(\rho )}$ 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.
LA - eng
KW - Krätzel integral transformation; $L_p$-spaces; distributions; Krätzel transformation; McBride space; distribution; generalized Laplace transformation
UR - http://eudml.org/doc/248244
ER -

References

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  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. (1991) 
  3. Erdelyi A., Magnus W., Oberhettinger F., Tricomi F., Tables of Integral Transforms, Vol. II, McGraw-Hill, New York, 1954. Zbl0058.34103MR0065685
  4. Kilbas A.A., Bonilla B., Rivero M., Rodríguez J., Trujillo J., Bessel type function and Bessel type integral transform on spaces ℱ p , μ and ℱ p , μ ' , to appear. 
  5. Krätzel E., Eine verallgemeinerung der Laplace- und Meijer-transformation, Wiss. Z. Univ. Jena Math. Naturw. Reihe 5 (1965), 369-381. (1965) MR0231142
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  7. Krätzel E., Integral transformations of Bessel-type, Proceeding of International Conference on Generalized Functions and Operational Calculus, Varna, 1975, pp.148-155. MR0547343
  8. Krätzel E., Menzer H., Verallgemeinerte Hankel-Funktionen, Pub. Math. Debrecen 18, fasc. 1-4 (1973), 139-148. (1973) MR0310309
  9. McBride A.C., Fractional Calculus and Integral Transforms of Generalized Functions, Res. Notes Math., 31, Pitman Press, San Francisco, London, Melbourne, 1979. Zbl0423.46029MR0550881
  10. McBride A.C., Fractional powers of a class ordinary differential operators, Proc. London Math. Soc., Ser. 3 45 (1982), 3 519-546. (1982) MR0675420
  11. Rao G.L.N., Debnath L., A generalized Meijer transformation, Int. J. Math. & Math. Sci. 8:2 (1985), 359-365. (1985) Zbl0597.46036MR0797835
  12. Zemanian A.H., A distributional K transformation, Siam J. Appl. Math. 14 6 (1966), 1350-1365. (1966) 
  13. Zemanian A.H, Generalized Integral Transformation, Interscience Publisher, New York, 1968. MR0423007

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