On defining the generalized functions δ α ( z ) and δ n ( x )

E. K. Koh and C. K. Li

International Journal of Mathematics and Mathematical Sciences, 1993, vol. 16, 1-6

Abstract:

In a previous paper (see [5]), we applied a fixed δ -sequence and neutrix limit due to Van der Corput to give meaning to distributions δ k and ( δ ′ ) k for k ∈ ( 0 , 1 ) and k = 2 , 3 , … . In this paper, we choose a fixed analytic branch such that z α ( − π < arg z ≤ π ) is an analytic single-valued function and define δ α ( z ) on a suitable function space I a . We show that δ α ( z ) ∈ I ′ a . Similar results on ( δ ( m ) ( z ) ) α are obtained. Finally, we use the Hilbert integral φ ( z ) = 1 π i ∫ − ∞ + ∞ φ ( t ) t − z d t where φ ( t ) ∈ D ( R ) , to redefine δ n ( x ) as a boundary value of δ n ( z − i ϵ ) . The definition of δ n ( x ) is independent of the choice of δ -sequence.

Date: 1993
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/16/927264.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/16/927264.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:927264

DOI: 10.1155/S0161171293000936

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().