On the Polyconvolution with the Weight Function for the Fourier Cosine, Fourier Sine, and the Kontorovich-Lebedev Integral Transforms

Nguyen Xuan Thao

Mathematical Problems in Engineering, 2010, vol. 2010, 1-16

Abstract:

The polyconvolution with the weight function ð ›¾ of three functions ð ‘“ , ð ‘” , and â„Ž for the integral transforms Fourier sine ( ð ¹ ð ‘ ) , Fourier cosine ( ð ¹ ð ‘ ) , and Kontorovich-Lebedev ( ð ¾ ð ‘– 𠑦 ) , which is denoted by ð ›¾ ∗ ( ð ‘“ , ð ‘” , â„Ž ) (x) , has been constructed. This polyconvolution satisfies the following factorization property ð ¹ ð ‘ ( ð ›¾ ∗ ( ð ‘“ , ð ‘” , â„Ž ) ) ( 𠑦 ) = s i n 0 ð ‘¥ 0 0 0 ð ‘Ž 0 𠑦 ( ð ¹ ð ‘ ð ‘“ ) ( 𠑦 ) â‹… ( ð ¹ ð ‘ ð ‘” ) ( 𠑦 ) â‹… ( ð ¾ ð ‘– 𠑦 â„Ž ) ( 𠑦 ) , for all 𠑦 > 0 . The relation of this polyconvolution to the Fourier convolution and the Fourier cosine convolution has been obtained. Also, the relations between the polyconvolution product and others convolution product have been established. In application, we consider a class of integral equations with Toeplitz plus Hankel kernel whose solution in closed form can be obtained with the help of the new polyconvolution. An application on solving systems of integral equations is also obtained.

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2010/709607.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2010/709607.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:jnlmpe:709607

DOI: 10.1155/2010/709607

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().