Sets of uniqueness

Thomas W. Körner

Cahiers du séminaire d'histoire des mathématiques (1992)

  • Volume: 2, page 51-63
  • ISSN: 0767-7421

How to cite

top

Körner, Thomas W.. "Sets of uniqueness." Cahiers du séminaire d'histoire des mathématiques 2 (1992): 51-63. <http://eudml.org/doc/91031>.

@article{Körner1992,
author = {Körner, Thomas W.},
journal = {Cahiers du séminaire d'histoire des mathématiques},
language = {eng},
pages = {51-63},
publisher = {Institut Henri Poincaré, Séminaire d'histoire des mathématiques : Paris},
title = {Sets of uniqueness},
url = {http://eudml.org/doc/91031},
volume = {2},
year = {1992},
}

TY - JOUR
AU - Körner, Thomas W.
TI - Sets of uniqueness
JO - Cahiers du séminaire d'histoire des mathématiques
PY - 1992
PB - Institut Henri Poincaré, Séminaire d'histoire des mathématiques : Paris
VL - 2
SP - 51
EP - 63
LA - eng
UR - http://eudml.org/doc/91031
ER -

References

top
  1. [1] N.K. Bari. Sur l'unicité du dévelloppement trigonométrique. CRASP, 177:62-118, 1923. JFM49.0198.09
  2. [2] N.K. Bari. Sur le rôle des lois diophantiques dans le problème d'unicité du dévelloppement trigonométrique. Mat Sbornik, 2 (44):699-722, 1937. Zbl0018.01801
  3. [3] N.K. Bari. A Treatise on Trigonometric Series. Fizmatgiz, 1961. In Russian. An English translation was published by Pergamon in 1964. Zbl0129.28002MR126115
  4. [4] G. Cantor. Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Springer, 1932. Zbl0004.05401MR616083
  5. [5] J.W. Dauben. Georg Cantor. Harvard UP, 1979. Zbl0463.01009MR525577
  6. [6] P.G.L. Dirichlet. Sur la convergence des séries trigonométriques. Jour, für Math., 4, 1829. Reprinted in his Collected Works. 
  7. [7] P. Du Bois-Reymond. Nachrichten König. Ges. der Wiss. zu Gött., pages 571-82, 1873. 
  8. [8] J.P. Kahane and R. Salem. Ensembles parfaits et séries trigonométriques. Hermann, 1963. Zbl0112.29304MR160065
  9. [9] R. Kaufman. M-sets and distributions. Astérisque, 5:225-230, 1973. Zbl0281.43006MR404975
  10. [10] R. Kaufman. Fourier transforms and discriptive set theory. Mathematika, 31:336-339, 1984. Zbl0604.42009MR804207
  11. [11] A.S. Kechris and A. Louveau. Descriptive Set Theory and the Structure of Sets of Uniqueness. CUP, 1987. Zbl0642.42014MR953784
  12. [12] T.W. Körner. A pseudofunction on a helson set i and ii. Astérisque, 5:3-224 and 231-239, 1973. Zbl0281.43005MR404974
  13. [13] H. Lebesgue. Leçons sur les séries trigonométriques. Gauthier-Villars, 1906. Zbl37.0281.01JFM37.0281.01
  14. [14] P. Malliavin. Impossibilité de la synthése spectrale sur les groupes abéliens non compacts. Publ. Math. IHES, pages 61-68, 1959. Zbl0101.09403MR107126
  15. [15] P. Malliavin. Ensembles de résolution spectrale. Proc. Internat. Congr. Math., pages 368-378, 1962. Zbl0135.35303MR179540
  16. [16] B. Mandelbrot. The Fractal Geometry of Nature. W.H.Freeman, 1977. Extended version of Les Objects Fractals (Flammarion 1975). Zbl0504.28001MR665254
  17. [17] S. Mazurkiewicz. Über die menge der differenzierbaren functionen. Fund. Math., 27:244-249, 1936. Zbl0015.20503
  18. [18] D.E. MensǓv. Sur l'unicité du dévelloppement trigonométrique. CRASP, 163:433-436, 1916. JFM46.0457.02
  19. [19] Iva_ev-Musatov O.S.On the fourier-stieljes coefficients of singular functions. Dokl. Akad. Nauk. SSSR (N.S.), 82:9-11, 1952. In Russian. There is an translation in the Amer. Math. Soc. Translation Séries. Zbl0046.06703MR49377
  20. [20] Piatetski-Shapiro. Supplement to the work' on the problems of uniqueness of expansion of a function in trigonometric series'. Moscov. Gos. Univ. Uč. Zap., 165, Mat 7:79-97, 1954. In Russian. There is an translation in the Amer. Math. Soc. Translation Series. MR67226
  21. [21] A. Rajchman. Sur l'unicité du dévelloppement trigonométrique. Fund Math, 3:286-302, 1922. Zbl48.0304.03JFM48.0304.03
  22. [22] G.F.B. Riemann. Habilitatsionschrift. Abh. der Ges. der Wiss. zu Gött., 13:87-132, 1868. Reprinted in his Collected Works. 
  23. [23] R. Salem. Sets of uniqueness and sets of multiplicity. Trans AMS, 54:218-228, 1943. Only part of this paper is correct. Corrections appear on pages 595-598 of Trans AMS, vol 63 (1948). Or see Salem's Collected Works. Zbl0060.18605MR8428
  24. [24] R. Salem and A. Zygmund. Sur un théorème de piatetski-shapiro. CRASP, 240:2040-2042, 1954. Zbl0065.29702MR71580
  25. [25] Rudin W.Fourier-stieljes transforms of measures on independent sets. Bull. Amer. Math. Soc., 66:199-202, 1960. Zbl0099.32201MR119035
  26. [26] W.H. Young. A note on trigonometric series. Mess, for Maths., 38:44-48, 1909. JFM39.0323.01
  27. [27] A. Zygmund. Trigonometric Series. CUP, 2nd edition, 1959. Zbl0085.05601

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.