Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter September 3, 2014

Extending the Stieltjes transform II

Dennis Nemzer


The Stieltjes transform has recently been extended to a subspace of Boehmians. In this note, additional results are obtained which include an inversion formula plus Abelian type theorems.

[1] R.D. Carmichael and E.O. Milton, Abelian theorems for the distributional Stieltjes transform. J. Math. Anal. Appl. 72 (1979), 195–205. in Google Scholar

[2] G. Doetsch, Handbuch der Laplace-Transformation, Vol. I. Verlag Birkhauser, Basel (1950). in Google Scholar

[3] V. Marić, M. Skendžić, and A. Takači, On Stieltjes transform of distributions behaving as regular varying functions. Acta Sci. Math. 50 (1986), 405–410. Search in Google Scholar

[4] P. Mikusiński, Convergence of Boehmians. Japan. J. Math. (N.S.) 9 (1983), 159–179. Search in Google Scholar

[5] P. Mikusiński, A. Morse, and D. Nemzer, The two-sided Laplace transform for Boehmians. Integ. Trans. Spec. Func. 2 (1994), 219–230. in Google Scholar

[6] O.P. Misra and J.L. Lavoine, Transform Analysis of Generalized Functions. Elsevier Science Publishers, Amsterdam (1986). Search in Google Scholar

[7] D. Nemzer, The Laplace transform on a class of Boehmians. Bull. Austral. Math. Soc. 46 (1992), 347–352. in Google Scholar

[8] D. Nemzer, A note on the convergence of a series in the space of Boehmians. Bull. Pure Appl. Math. 2 (2008), 63–69. Search in Google Scholar

[9] D. Nemzer, Extending the Stieltjes transform. Sarajevo J. Math., Accepted. Search in Google Scholar

[10] D. Nikolić-Despotović and S. Pilipović, Abelian theorem for the distributional Stieltjes transformation. In: Generalized Functions, Convergence Structures and Their Applications (Proc. Intern. Conf. Dubrovnik, 1987), Plenum Press, New York and London (1988), 269–277. 10.1007/978-1-4613-1055-6_13Search in Google Scholar

[11] S. Pilipović, B. Stanković, and A. Takači, Asymptotic Behaviour and Stieltjes Transformation of Distributions. Taubner, Leipzig (1990). Search in Google Scholar

[12] A.H. Zemanian, Inversion formulas for the distributional Laplace transformation. J. SIAM Appl. Math. 14 (1966), 159–166. in Google Scholar

[13] A.H. Zemanian, Distribution Theory and Transform Analysis. Dover Publications, New York (1987). Search in Google Scholar

Published Online: 2014-9-3
Published in Print: 2014-12-1

© 2014 Diogenes Co., Sofia

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow