Quaternion Stieltjes Transform and Quaternion Laplace-Stieltjes Transform

Authors

  • Khinal Parmar Department of Basic Science and Humanities, NMIMS, MPSTME, Mumbai
  • V. R. Lakshmi Gorty Department of Basic Science and Humanities, NMIMS, MPSTME, Mumbai

DOI:

https://doi.org/10.26713/cma.v12i3.1532

Keywords:

Quaternion Stieltjes transform, Quaternion Laplace-Stieltjes transform, Convolution theorem, Applications

Abstract

In this study, we introduce quaternion Stieltjes transform. Various properties of the quaternion Stieltjes transform are derived. We also define quaternion Laplace-Stieltjes transform and operational properties of quaternion Laplace-Stieltjes transform are established. The theory is supported with applications in mathematical physics.

Downloads

Download data is not yet available.

References

C. J. K. Batty, Tauberian theorems for the Laplace-Stieltjes transform, Transactions of the American Mathematical Society 322 (1990), 783 – 804, DOI: 10.1090/S0002-9947-1990-1013326-6.

L. Debnath and D. Bhatta, Integral Transforms and Their Applications, 2nd edition, CRC Press (2006), DOI: 10.1201/9781420010916.

G. Han, Quaternionic slice regular functions and quaternionic Laplace transforms, arXiv:2006.07511 (2020), URL: https://arxiv.org/pdf/2006.07511.pdf.

F. Hirsch, Intégrales de résolvantes et calcul symbolique, Annales de l'insitut Fourier 22 (1972), 239 – 264, DOI: 10.5802/aif.439.

E. M. S. Hitzer, Quaternion Fourier transform on quaternion fields and generalizations, Advances in Applied Clifford Algebras 17 (2007), 497 – 517, DOI: 10.1007/s00006-007-0037-8.

S. Osaki, Applied Stochastic System Modelling, Springer-Verlag, Berlin ” Heidelberg (1992), DOI: 10.1007/978-3-642-84681-6.

R. S. Pathak and L. Debnath, Recent developments on the Stieltjes transform of generalized functions, International Journal of Mathematics and Mathematical Sciences 10 (1987), 641 – 670, Article ID 690826, DOI: 10.1155/S0161171287000784.

R. Roopkumar, Stieltjes transform for Boehmians, Integral Transforms and Special Functions 18 (2007), 845 – 853, DOI: 10.1080/10652460701510642.

R. Roopkumar, Quaternionic one-dimensional fractional Fourier transform, Optik 127 (2016), 11657 – 11661, DOI: 10.1016/j.ijleo.2016.09.069.

D. Saltz, An inversion theorem for Laplace-Stieltjes transforms, Pacific Journal of Mathematics 10 (1960), 309 – 312, DOI: 10.2140/pjm.1960.10.309.

J. H. Schwarz, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics 46 (2005), 013501, DOI: 10.1063/1.1825077.

D. V. Widder, The Laplace Transform, Princeton University Press (1946), DOI: 10.1515/9781400876457.

D. V. Widder, The Stieltjes transform, Transactions of the American Mathematical Society 43 (1938), 7 – 60, DOI: 10.1090/S0002-9947-1938-1501933-2.

H. Y. Xu and Z. X. Xuan, The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane, Journal of Inequalities and Applications 2013 (2013), Article number: 273, DOI: 10.1186/1029-242X-2013-273.

K. Yinying and S. Daochun, On the growth of zero order Laplace-Stieltjes transform convergent in the right half-plane, Acta Mathematica Scientia 28 (2008), 431 – 440, DOI: 10.1016/S0252-9602(08)60045-4.

Downloads

Published

30-09-2021
CITATION

How to Cite

Parmar, K., & Gorty, V. R. L. (2021). Quaternion Stieltjes Transform and Quaternion Laplace-Stieltjes Transform. Communications in Mathematics and Applications, 12(3), 633–643. https://doi.org/10.26713/cma.v12i3.1532

Issue

Section

Research Article