Version 1
: Received: 30 August 2024 / Approved: 1 September 2024 / Online: 2 September 2024 (12:05:55 CEST)
How to cite:
Mandelkern, J. A Novel Spectral Density Function Validation for Bessel’s Equation in L-N Form. Preprints2024, 2024090060. https://doi.org/10.20944/preprints202409.0060.v1
Mandelkern, J. A Novel Spectral Density Function Validation for Bessel’s Equation in L-N Form. Preprints 2024, 2024090060. https://doi.org/10.20944/preprints202409.0060.v1
Mandelkern, J. A Novel Spectral Density Function Validation for Bessel’s Equation in L-N Form. Preprints2024, 2024090060. https://doi.org/10.20944/preprints202409.0060.v1
APA Style
Mandelkern, J. (2024). A Novel Spectral Density Function Validation for Bessel’s Equation in L-N Form. Preprints. https://doi.org/10.20944/preprints202409.0060.v1
Chicago/Turabian Style
Mandelkern, J. 2024 "A Novel Spectral Density Function Validation for Bessel’s Equation in L-N Form" Preprints. https://doi.org/10.20944/preprints202409.0060.v1
Abstract
In the 2014 paper by C. Fulton, D. Pearson, and S. Pruess [7], a new characterization of the spectral density function is given for a Sturm-Liouville equation. These authors provide spectral theory showing that the Appell system, a companion linear system of ordinary differential equations, can be utilized to obtain a spectral density function. Though this new method is both elegant for its simplicity and fully viable (as is shown in this work), it has largely been ignored in the literature since its discovery. To motivate greater attention towards this new theory, and its potential applications, work is given here by this author demonstrating a nontrivial example of this new spectral method being applied towards the Bessel Equation in its Liouville-Normal (L-N) form. Validations of results obtained in this paper are also given, showing full agreement with the classical results obtained by E.C. Titchmarsh in [11].
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
