Some Abelian and Tauberian Theorems

  • Richard M. Meyer
Part of the Universitext book series (UTX)


As an immediate application of the results of the preceding Sections we now consider briefly some Examples of what are known as Abelian and Tauberian-type Theorems. These results have found use in a variety of Applied fields.


Asymptotic Behavior Power Series Vary Function Slow Variation Laplace Transform 
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References to Additional and Related Material: Section 7

  1. 1.
    Feller, W., “An Introduction to Probability Theory and its Applications”, Vol. II, John Wiley and Sons, Inc. (1966).Google Scholar
  2. 2.
    Ford, W., “Divergent Series”, Chelsea Publishing Co., Inc. (1960).Google Scholar
  3. 3.
    Grimm, C., “A Unified Method of Finding Laplace Transforms, Fourier Transforms, and Fourier Series”, U.M.A.P. Unit 324, Educational Development Center, Newton, Massachusetts (1978).Google Scholar
  4. 4.
    Hobson, E., “Theory of Functions of a Real Variable”, Vol. II, Dover Publications, Inc.Google Scholar
  5. 5.
    Pitt, H., “Tauberian Theorems”, Oxford University Press. (1958).Google Scholar
  6. 6.
    Smith, W., Unpublished Lecture Notes, University of North Carolina (1964).Google Scholar
  7. 7.
    Spiegel, M., “Schaum’s Outline of Theory and Problems of Laplace Transforms”, Schaum Publishing Co. (1965).Google Scholar
  8. 8.
    Widder, D., “An Introduction to Transform Theory”, Academic Press (1971).Google Scholar
  9. 9.
    Widder, D., “The Laplace Transform”, Princeton University Press (1941).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1979

Authors and Affiliations

  • Richard M. Meyer
    • 1
  1. 1.Niagara University, College of Arts and SciencesNiagara UniversityUSA

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