Schwarz, John H. (2005) The generalized Stieltjes transform and its inverse. Journal of Mathematical Physics, 46 (1). Art. No. 013501. ISSN 0022-2488 http://resolver.caltech.edu/CaltechAUTHORS:SCHWjmp05
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Abstract
The generalized Stieltjes transform (GST) is an integral transform that depends on a parameter rho> 0. In previous work a convenient form of the inverse transformation was derived for the case rho= 3/2. This paper generalizes that result to all rho> 0. It is a well-known fact that the GST can be formulated as an iterated Laplace transform, and that therefore its inverse can be expressed as an iterated inverse Laplace transform. The form of the inverse transform derived here is a one-dimensional integral that is considerably simpler.
| Item Type: | Article |
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| Additional Information: | ©2005 American Institute of Physics (Received 3 June 2004; accepted 16 September 2004; published online 23 December 2004) The author is grateful to Y. H. He, M. Spradlin, and A. Volovich for their collaboration in Ref. 1, which contains the r =3/2 case of the result described here. This work was supported in part by the U.S. Department of Energy under Grant No. DE-FG03-92-ER40701. |
| Subject Keywords: | Laplace transforms; iterative methods; inverse problems; integral equations |
| Record Number: | CaltechAUTHORS:SCHWjmp05 |
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:SCHWjmp05 |
| Alternative URL: | http://dx.doi.org/10.1063/1.1825077 |
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 3061 |
| Collection: | CaltechAUTHORS |
| Deposited By: | Archive Administrator |
| Deposited On: | 12 May 2006 |
| Last Modified: | 26 Dec 2012 08:52 |
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