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On some criteria of Carleman for the complete convergence of a $J$-fraction


Author: H. S. Wall
Journal: Bull. Amer. Math. Soc. 54 (1948), 528-532
DOI: https://doi.org/10.1090/S0002-9904-1948-09033-4
MathSciNet review: 0025597
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References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. T. Carleman, Sur les équations intégrales singulières a noyau réel et symétrique, Uppsala, 1923.
  • 2. T. Carleman, Les fonctions quasi analytiques, Paris, 1926.
  • 3. J. J. Dennis and H. S. Wall, The limit-circle case for a positive definite J-fraction, Duke Math. J. vol. 12 (1945) pp. 255-273. MR 13436
  • 4. Hans Hamburger, Über eine Erweiterung des Stieltjesschen Momentenproblems, Math. Ann. 82 (1920), no. 1-2, 120–164 (German). MR 1511978, https://doi.org/10.1007/BF01457982
  • 5. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge, 1934. MR 46395
  • 6. Ernst Hellinger, Zur Stieltjesschen Kettenbruchtheorie, Math. Ann. 86 (1922), no. 1-2, 18–29 (German). MR 1512075, https://doi.org/10.1007/BF01458568
  • 7. E. Hellinger and H. S. Wall, Contributions to the analytic theory of continued fractions and infinite matrices, Ann. of Math. vol. 44 (1943) pp. 103-127. MR 8102
  • 8. W. T. Scott and H. S. Wall, On the convergence and divergence of continued fractions, Amer. J. Math. vol. 69 (1947) pp. 551-561. MR 21137
  • 9. T. J. Stieltjes, Sur la réduction en fraction continue d'une série procédant suivant es puissances descendantes d'une variable, Oeuvres, vol. 2, pp. 184-200.


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1948-09033-4

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