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Inversion and Representation Theorems for the Laplace Transformation


Rooney, Paul George (1952) Inversion and Representation Theorems for the Laplace Transformation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1WJR-ZQ41.


A study is made of the Laplace transformation on Banach-valued functions of a real variable, with particular reference to inversion and representation theories. First a new type of integral for Banach-valued functions of a real variable, the "Improper Bochner" integral is defined. The relations between the Bochner, Improper Bochner, Riemann-Graves, and Riemann-Stieltjes integrals are studied. Next, inversion theorems are proved for a new "real" inversion operator when the integral in the Laplace transformation is each of the above mentioned types. Lastly, representation of Banach-valued functions by Laplace integrals of functions in Bp([0,∞);¥), 1 ≤ p < ∞, is studied, and theorems are very like those proved, for numerically-valued functions, by D. V. Widder in his book "The Laplace Transform" (Princeton, 1941) page 312. The classes Hp(α ; ¥), 1 ≤ p < ∞, are also studied in this section as is the representation of numerically-valued functions by Laplace-Stieltjes integrals.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Erdélyi, Arthur
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1952
Record Number:CaltechTHESIS:12122017-142045730
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10602
Deposited By: Benjamin Perez
Deposited On:12 Dec 2017 23:22
Last Modified:16 May 2023 22:14

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