Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Operational calculus and the finite part of divergent integrals


Author: T. K. Boehme
Journal: Trans. Amer. Math. Soc. 106 (1963), 346-368
MSC: Primary 44.40
MathSciNet review: 0144165
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] Sur un nouveau genre d'integrales, Oeuvres complètes d'Augustin Cauchy, Series II, Vol. 6, pp. 78-88, Gauthier-Villars, Paris, 1938.
  • [2] Diverses proprietés de la fonction $ \Gamma (x)$, Oeuvres complètes d'Augustin Cauchy, Series II, Vol. 7, pp. 121-123, Gauthier-Villars, Paris, 1938.
  • [3] Jacques Hadamard, Lectures on Cauchy’s problem in linear partial differential equations, Dover Publications, New York, 1953. MR 0051411 (14,474f)
  • [4] Florent J. Bureau, Divergent integrals and partial differential equations, Comm. Pure Appl. Math. 8 (1955), 143–202. MR 0068085 (16,826a)
  • [5] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). MR 0209834 (35 #730)
  • [6] M. J. Lighthill, Introduction to Fourier analysis and generalised functions, Cambridge University Press, New York, 1960. MR 0115085 (22 #5888)
  • [7] P. L. Butzer, Singular integral equations of Volterra type and the finite part of divergent integrals, Arch. Rational Mech. Anal. 3 (1959), 194–205 (1959). MR 0107792 (21 #6514)
  • [8] J. Mikusiński, Operational calculus, Pergamon, New York, 1959.
  • [9] A. Erdélyi, Operational calculus and generalized function, California Institute of Technology, 1959. (Lecture notes)
  • [10] J. D. Weston, Operational calculus and generalized functions, Proc. Roy. Soc. London Ser. A 250 (1959), 460–471. MR 0104113 (21 #2875)
  • [11] J. D. Weston, An extension of the Laplace-transform calculus, Rend. Circ. Mat. Palermo (2) 6 (1957), 325–333. MR 0104109 (21 #2871)
  • [12] Jan G.- Mikusiński, Sur les fondements du calcul opératoire, Studia Math. 11 (1949), 41–70 (French). MR 0036949 (12,189d)
  • [13] C. Ryll-Nardzewski, Sur les séries de puissances dans le calcul opératoire, Studia Math. 13 (1953), 41–47 (French). MR 0055588 (14,1097c)
  • [14] A. Erdélyi, W. Magnus, F. Oberhettinger, F. Tricomi and Bateman staff, Higher transcendental functions, Vol. II, McGraw-Hill, New York, 1953.
  • [15] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of integral transforms. Vol. I, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954. Based, in part, on notes left by Harry Bateman. MR 0061695 (15,868a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 44.40

Retrieve articles in all journals with MSC: 44.40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1963-0144165-X
PII: S 0002-9947(1963)0144165-X
Article copyright: © Copyright 1963 American Mathematical Society