Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A class of sequences of functions


Author: D. G. Bourgin
Journal: Trans. Amer. Math. Soc. 60 (1946), 478-518
MSC: Primary 42.4X
DOI: https://doi.org/10.1090/S0002-9947-1946-0020168-0
MathSciNet review: 0020168
Full-text PDF

References | Similar Articles | Additional Information

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

  • [1] D. G. Bourgin and C. W. Mendel, Orthonormal sets of periodic functions of the type $ \{ f{(nx)}\} $, Trans. Amer. Math. Soc. vol. 57 (1945) pp. 332-363. MR 0012158 (6:266f)
  • [2] A. S. Besicovitch, Almost periodic functions, Cambridge University Press, 1932.
  • [3] H. Bohr, Über die Bedeutung der Potenzreihen unendlich vieler Variabein in der Theorie der Dirichletschen Reihen, Nachr. Ges. Wiss. Göttingen (1913) pp. 441-488.
  • [4] O. Toeplitz, Zu Theorie der Dirichlet Reihen, Amer. J. Math. vol. 60 (1938) pp. 880-888. MR 1507354
  • [5] A. Wintner, Spektratheorie der unendlichen Matrizen, Leipzig, 1929.
  • [6] L. Bieberbach, Moderne Funktionentheorie, 2d ed., Teubner, 1931.
  • [7] E. C. Titchmarsh, The theory of functions, 2d ed., Oxford University Press, 1939. MR 0197687 (33:5850)
  • [8] S. Banach, Théorie des opérations linéaries, Warsaw, 1932.
  • [9] P. Fatou, Serie trigonometrique et serie de Taylor, Acta Math. vol. 30 (1906) pp. 335-400.
  • [10] F. Riesz and M. Riesz, Über die Randwerte eines analytischen Funktion. Compte rendu au quatrième Congrès des mathematiciens Scandinaves, Stockholm, pp. 27-47.
  • [11] W. F. Osgood, Lehrbuch der Funktionentheorie, vol. 2, Teubner, 1924.
  • [12] G. N. Watson, General transforms, Proc. London Math. Soc. vol. 35 (1933) pp. 156-199.
  • [13] D. V. Widder, The Laplace transform, Princeton University Press, 1941. MR 0005923 (3:232d)
  • [14] O. Szász, Über die Approximation stetiger Funktionen durch gegebene Funktionenfolgen, Math. Ann. vol. 104 (1931) pp. 155-160. MR 1512657
  • [15] R. E. A. C. Paley and N. Wiener, Fourier transforms in the complex plane, Amer. Math. Soc. Colloquium Publications, vol. 19, 1934.
  • [16] D. G. Bourgin, Closure of products of functions, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 807-815. MR 0002676 (2:97d)
  • [17] O. Frink, Series expansions in linear vector spaces, Amer. J. Math. vol. 63 (1941) pp. 87-100. MR 0003452 (2:222b)
  • [18] R. J. Duffin and J. J. Eachus, Some notes on an expansion theorem of Paley and Wiener, Bull. Amer. Math. Soc. vol. 48 (1942) pp. 850-855. MR 0007173 (4:97e)
  • [19] E. Landau, Ergebnisse der Funktionentheorie, 2d ed., Springer, 1029.
  • [20] W. Seidel, On the distribution of values of bounded analytic functions, Trans. Amer. Math. Soc. vol. 36 (1934) pp. 201-226. MR 1501738

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42.4X

Retrieve articles in all journals with MSC: 42.4X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1946-0020168-0
Article copyright: © Copyright 1946 American Mathematical Society

American Mathematical Society