On the canonical development of Parseval formulas for singular differential operators

Robert W. Carroll

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1982)

  • Volume: 72, Issue: 2, page 65-70
  • ISSN: 0392-7881

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Carroll, Robert W.. "On the canonical development of Parseval formulas for singular differential operators." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 72.2 (1982): 65-70. <http://eudml.org/doc/288969>.

@article{Carroll1982,
author = {Carroll, Robert W.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {2},
number = {2},
pages = {65-70},
publisher = {Accademia Nazionale dei Lincei},
title = {On the canonical development of Parseval formulas for singular differential operators},
url = {http://eudml.org/doc/288969},
volume = {72},
year = {1982},
}

TY - JOUR
AU - Carroll, Robert W.
TI - On the canonical development of Parseval formulas for singular differential operators
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1982/2//
PB - Accademia Nazionale dei Lincei
VL - 72
IS - 2
SP - 65
EP - 70
LA - eng
UR - http://eudml.org/doc/288969
ER -

References

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  1. Carroll, R. (1979) - Transmutation and operator differential equations, «Notas de Matematica», 67, North-Holland, Amsterdam. Zbl0416.35021
  2. Carroll, R. (1979) - Transmutation, Parseval formulas, and generalized spectral functions, «Notices Amer. Math. Soc.», Aug., A434 - Transmutation, generalized translation, and transform theory, I and II, Osaka Jour. Math., to appear. 
  3. Carroll, R. (1979) - Some remarks on transmutation, «Applicable Anal.», 9, 291-294. Zbl0435.34010
  4. Carroll, R. - Transmutation, scattering theory, and special functions, North-Holland, Amsterdam, 1982. 
  5. Carroll, R. (1981) - Remarks on the Gelfand-Levitan and Marčenko equations, «Applicable Anal.», 7, 153-157. Zbl0501.34025
  6. Carroll, R. - The Gelfand-Levitan and Marčenko equations via transmutation, «Rocky Mount. Jour. Math.», 12 (1982), 393-427. 
  7. Carroll, R. - Some remarks on the generalized Gelfand-Levitan equation, «Jour. Math. Anal. Appl.», to appear. 
  8. Carroll, R. (1981) - A survey of some recent results in transmutation, «Spectral Theory of Differential Operators», North-Holland, pp. 81-92. 
  9. Carroll, R. - Elliptic transmutation, I, «Proc. Royal Soc.»Edinburgh, 91A (1982), 315-334. 
  10. Carroll, R. (1981) - Some remarks on singular pseudodifferential operators, «Comm. Partial Diff. Eqs.», 6 (12), 1907-1927. 
  11. Carroll, R. - Some inversion theorems of Fourier type, «Rev. Roumaine Math. Pures Appl.», to appear. 
  12. Carroll, R. - On the characterization of transmutations, «Anais Acad. Brasil. Ciencias», 54 (1982), 271-280. 
  13. Carroll, R. and Gilbert, J. (1981) - Scattering techniques in transmutation and some connection formulas for special functions, «Proc. Japan Acad.», 57, 34-37. Zbl0477.34020
  14. Carroll, R. and Gilbert, J. (1981) - Remarks on transmutation, scattering theory, and special functions, «Math Annalen», 258, 39-54. Zbl0457.33005MR641667DOI10.1007/BF01450345
  15. Carroll, R. and Santosa, F. (1981) - Résolution d'un problème inverse qui détermine complètement les données géophysiques, «C. R. Acad. Sci. Paris», 292, 23-26. Zbl0545.35091
  16. Carroll, R. and Santosa, F. (1981) - Scattering techniques for a one dimensional inverse problem in geophysics, «Math. Methods Appl. Sci.», 3, 145-171. Zbl0456.73086
  17. Chebli, H. (1979) - Théorème de Paley-Wiener associé à un opérateur différentiel singulier sur ( 0 , ) , «Jour. Math. Pures Appl.», 58, 1-19. Zbl0362.34019
  18. Flensted-Jensen, M. (1972) - Paley-Wiener type theorems for a differential operator connected with symmetric spaces, «Ark Math.», 10, 143-162. Zbl0233.42012
  19. Gasymov, M. (1975) - The expansion in eigenfunctions for a nonselfadjoint second order differential operator with a singularity at zero. «Trudy Let. Šk. Spekt. Teorii Oper.»..., Izd. Aim, Baku, pp. 20-45. 
  20. Koornwinder, T. (1975) - A new proof of a Paley-Wiener type theorem for the Jacobi transform, «Ark. Mat.», 13, 145-159. Zbl0303.42022
  21. Levitan, B. (1973) - The theory of generalized translation operators, «Izd. Nauka», Moscow. 
  22. Lions, J. (1956) - Opérateurs de Delsarte et problèmes mixtes, «Bull. Soc. Math. France», 84, 9-95. Zbl0075.10804
  23. Marcenko, V. (1977) - Sturm-Liouville operators and their applications, «Izd. Nauk». Dumka, Kiev. 
  24. Siersma, J. (1979) - On a class of singular Cauchy problems, «Thesis», Groningen. 
  25. Trimeche, K. (1981) - Transformation intégrale de Weyl et théorème de Paley-Wiener associés à un opérateur différentiel singulier sur ( 0 , ) , «Jour. Math. Pures Appl.», 60, 51-98. Zbl0416.44002

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