On the transformation theory of ordinary second-order linear symmetric differential expressions

William Norrie Everitt

Czechoslovak Mathematical Journal (1982)

  • Volume: 32, Issue: 2, page 275-306
  • ISSN: 0011-4642

How to cite

top

Everitt, William Norrie. "On the transformation theory of ordinary second-order linear symmetric differential expressions." Czechoslovak Mathematical Journal 32.2 (1982): 275-306. <http://eudml.org/doc/13312>.

@article{Everitt1982,
author = {Everitt, William Norrie},
journal = {Czechoslovak Mathematical Journal},
keywords = {second-order linear symmetric differential expressions; isometric transformations; Liouville-transformation},
language = {eng},
number = {2},
pages = {275-306},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the transformation theory of ordinary second-order linear symmetric differential expressions},
url = {http://eudml.org/doc/13312},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Everitt, William Norrie
TI - On the transformation theory of ordinary second-order linear symmetric differential expressions
JO - Czechoslovak Mathematical Journal
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 2
SP - 275
EP - 306
LA - eng
KW - second-order linear symmetric differential expressions; isometric transformations; Liouville-transformation
UR - http://eudml.org/doc/13312
ER -

References

top
  1. С. D. Ahlbrandt, 10.1016/0022-0396(69)90018-7, J. Diff. Equations 6 (1969), 271-295. (1969) Zbl0175.09301MR0244541DOI10.1016/0022-0396(69)90018-7
  2. N. I. Akhiezer, I. M. Glazman, Theory of linear operators in Hilbert space: Volume I, (Ungar; New York, 1961). (1961) Zbl0098.30702MR0264420
  3. F. V. Atkinson, Discrete and continuous boundary problems, (Academic Press; New York, 1964). (1964) Zbl0117.05806MR0176141
  4. C. Bennewitz, W. N. Everitt, Some remarks on the Titchmarsh-Weyl m -coefficient, In: Tribute to Åke Pleijel: Proceedings of the Pleijel Conference, University of Uppsala (1979), 49-108. (Published by the Department of Mathematics, University of Uppsala, Sweden, in 1980). (1979) 
  5. G. Birkhoff, Gian-Carlo Rota, Ordinary differential equations, (Ginn and Company, New York, 1962). (1962) Zbl0102.29901MR0138810
  6. O. Borůvka, Linear differential transformations of the second order, (English Universities Press; London, 1971; translated from the German edition of 1967). (1971) Zbl0222.34002MR0463539
  7. N. Dunford, J. T. Schwartz, Linear operators: Part II, (Interscience Publishers; New York, 1963). (1963) Zbl0128.34803MR0188745
  8. M. S. P. Eastham, Theory of ordinary differential equations, (Van Nostrand Reinhold Company; London, 1970). (1970) Zbl0195.37001
  9. M. S. P. Eastham, The spectral theory of periodic differential equations, (Scottish Academic Press; Edinburgh, 1973). (1973) Zbl0287.34016
  10. W. N. Everitt, On a property of the m -coefficient of a second-order linear differential equation, J. London Math. Soc. (2) 4 (1972), 443-457. (1972) Zbl0262.34012MR0298104
  11. W. N. Everitt, 10.1007/BFb0065546, Lecture Notes in Mathematics 415 (1974), 338-352. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). (1974) Zbl0307.34013MR0419919DOI10.1007/BFb0065546
  12. W. N. Everitt, A note on the Dirichlet condition for second-order differential expressions, Canadian J. Math. XXVII (1916), 312-320. (1916) MR0430391
  13. W. N. Everitt, 10.1080/16073606.1978.9631547, Quaestiones Mathematicae 2 (1978), 479-494. (1978) Zbl0396.26006MR0486761DOI10.1080/16073606.1978.9631547
  14. W. N. Everitt M. Giertz, J. B. McLeod, On the strong and weak limit-point classification of second-order differential expressions, Proc. London Math. Soc. (3) 29 (1974), 142-158. (1974) Zbl0302.34022MR0361255
  15. W. N. Everitt, S. G. Halvorsen, 10.1080/00036817808839223, Applicable Analysis 8 (1978), 153 - 169. (1978) Zbl0406.34047MR0523952DOI10.1080/00036817808839223
  16. W. N. Everitt, D. Race, 10.1080/16073606.1978.9631549, Quaestiones Mathematicae 2 (1978), 507-512. (1978) Zbl0392.34002MR0477222DOI10.1080/16073606.1978.9631549
  17. W. N. Everitt, A. Zettl, Generalized symmetric ordinary differential expressions I: the general theory, Nieuw Archief voor Wiskunde (3) XXVII (1979), 363-397. (1979) Zbl0451.34009MR0553264
  18. W. N. Everitt, A. Zettl, 10.1112/jlms/s2-17.2.291, J. London Math. Soc. (2) 17 (1978), 291-303. (1978) Zbl0388.26007MR0477234DOI10.1112/jlms/s2-17.2.291
  19. E. Hille, Lectures on ordinary differential equations, (Addison-Wesley; London, 1969). (1969) Zbl0179.40301MR0249698
  20. D. B. Hinton, 10.1007/BFb0065526, Lecture Notes in Mathematics 415 (1974), 173 - 183. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). (1974) Zbl0337.34019MR0425236DOI10.1007/BFb0065526
  21. E. L. Ince, Ordinary differential equations, (Dover Publications, Inc.: New York, 1956; original edition, 1926). (1956) Zbl0063.02971MR0010757
  22. H. Kalf, 10.1007/BF01350583, Math. Ann. 210 (1974), 197-205. (1974) Zbl0297.34019MR0355177DOI10.1007/BF01350583
  23. M. A. Naimark, Linear differential operators: Part II, (Ungar; New York, 1968). (1968) Zbl0227.34020
  24. F. Neuman, On the Liouville transformation, Rendiconti di Matematica 3 (1970), 132-139. (1970) Zbl0241.34005MR0273090
  25. F. Neuman, On a problem of transformations between limit-point and limit-circle differential equations, Proc. Royal. Soc. Edinburgh 72 (1973/74), 187-193. (1973) MR0385226
  26. K. S. Ong, On the limit-point and limit-circle theory of a second-order differential equation, Proc. Royal Soc. Edinburgh 72 (1975), 245-256. (1975) Zbl0335.34012MR0393635
  27. Å. Pleijel, 10.1007/BFb0065531, Lecture Notes in Mathematics 415 (1974), 211 - 226. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). (1974) Zbl0301.34025MR0422741DOI10.1007/BFb0065531
  28. W. T. Reid, Ordinary differential equations, (Wiley and Sons, Inc.; New York, 1971). (1971) Zbl0212.10901MR0273082
  29. E. C. Titchmarsh, Eigenfunction expansions; Part I, (Oxford University Press, 1962). (1962) Zbl0099.05201MR0176151
  30. R. Weinstock, Calculus of variations, (McGraw-Hill; New York, 1952), (1952) Zbl0049.19503
  31. A. Zettl, 10.1216/RMJ-1975-5-3-453, Rocky Mountain J. of Math. 5 (1975), 453-474. (1975) MR0379976DOI10.1216/RMJ-1975-5-3-453

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.