Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Construction of characteristic functions for classes of infinitely differentiable functions
HTML articles powered by AMS MathViewer

by M. Allouche, R. Couture and C. T. Tsai PDF
Proc. Amer. Math. Soc. 111 (1991), 119-126 Request permission

Abstract:

Characteristic functions are constructed for classes of infinitely differentiable functions defined on a half-line and for Paley-Wiener classes. A corresponding result is given for normal operators defined in Hilbert space.
References
  • Shmuel Agmon, Sur l’équivalence des classes de fonctions indéfiniment dérivables sur un demi-axe, C. R. Acad. Sci. Paris 230 (1950), 350–352 (French). MR 32707
    • M. Allouche, Fonctions caractéristiques de certaines classes de fonctions indéfiniment dérivables, Thesis, Québec, 1986.
  • Thøger Bang, Om quasi-analytiske Funktioner, University of Copenhagen, Copenhagen, 1946 (Danish). Thesis. MR 0017782
  • Henri Cartan, Sur les maxima des dérivées successives d’une fonction, C. R. Acad. Sci. Paris 210 (1940), 431–434 (French). MR 1784
    • R. Couture, Classes de fonctions ${C^\infty }$ et approximation par des sommes d’exponentielles, Thesis, Québec, 1980.
  • A. Gorny, Contribution à l’étude des fonctions dérivables d’une variable réelle, Acta Math. 71 (1939), 317–358 (French). MR 848, DOI 10.1007/BF02547758
    • V. I. Korenbljum, Conditions of nontriviality of certain classes of functions analytic in a sector, and problems of quasianalyticity, Soviet Math. Dokl. 7 (1966), 232-236. S. Mandelbrojt, Sur l’équivalence de deux classes de fonctions de M. M. Paley et Wiener, C.R. Acad. Sci. Paris 204 (1937), 1860-1863.
  • S. Mandelbrojt, Une inégalité fondamentale, Ann. Sci. École Norm. Sup. (3) 43 (1947), 351–378 (French). MR 0022585
    • —, Séries adhérentes, régularisation des suites, applications, Gauthier Villars, Paris, 1952. G. Mittag-Leffier, Sur la représentation arithmétique des fonctions analytiques d’une variable complexe, Internat. Congress, 1908, pp. 67-85.
  • R. E. A. C. Paley and N. Wiener, Notes on the theory and application of Fourier transforms. I, II, Trans. Amer. Math. Soc. 35 (1933), no. 2, 348–355. MR 1501688, DOI 10.1090/S0002-9947-1933-1501688-7
  • E. M. Stein, Functions of exponential type, Ann. of Math. (2) 65 (1957), 582–592. MR 85342, DOI 10.2307/1970066
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26E10, 47B15
  • Retrieve articles in all journals with MSC: 26E10, 47B15
Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 111 (1991), 119-126
  • MSC: Primary 26E10; Secondary 47B15
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1045584-2
  • MathSciNet review: 1045584