Abstract
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.
Similar content being viewed by others
References
R.D. Carmichael and E.O. Milton, Abelian theorems for the distributional Stieltjes transform. J. Math. Anal. Appl. 72 (1979), 195–205.
G. Doetsch, Handbuch der Laplace-Transformation, Vol. I. Verlag Birkhauser, Basel (1950).
V. Marić, M. Skendžić, and A. Takači, On Stieltjes transform of distributions behaving as regular varying functions. Acta Sci. Math. 50 (1986), 405–410.
P. Mikusiński, Convergence of Boehmians. Japan. J. Math. (N.S.) 9 (1983), 159–179.
P. Mikusiński, A. Morse, and D. Nemzer, The two-sided Laplace transform for Boehmians. Integ. Trans. Spec. Func. 2 (1994), 219–230.
O.P. Misra and J.L. Lavoine, Transform Analysis of Generalized Functions. Elsevier Science Publishers, Amsterdam (1986).
D. Nemzer, The Laplace transform on a class of Boehmians. Bull. Austral. Math. Soc. 46 (1992), 347–352.
D. Nemzer, A note on the convergence of a series in the space of Boehmians. Bull. Pure Appl. Math. 2 (2008), 63–69.
D. Nemzer, Extending the Stieltjes transform. Sarajevo J. Math., Accepted.
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.
S. Pilipović, B. Stanković, and A. Takači, Asymptotic Behaviour and Stieltjes Transformation of Distributions. Taubner, Leipzig (1990).
A.H. Zemanian, Inversion formulas for the distributional Laplace transformation. J. SIAM Appl. Math. 14 (1966), 159–166.
A.H. Zemanian, Distribution Theory and Transform Analysis. Dover Publications, New York (1987).
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor Ivan Dimovski on the occasion of his 80th anniversary
About this article
Cite this article
Nemzer, D. Extending the Stieltjes transform II. Fract Calc Appl Anal 17, 1060–1074 (2014). https://doi.org/10.2478/s13540-014-0214-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s13540-014-0214-0