Integral Transforms Related to a Generalized Convolution

Results in Mathematics

Volumn 38, Issue 3-4, 2000, Pages 197-208

  Al Musallam, F ^a   Tuan, Vu Kim ^a  

^a KUWAIT UNIVERSITY   (Kuwait)

Author keywords

convolution; Fourier cosine transform; Fourier sine transform; integral transformation; unitary transformation

Indexed keywords

EID: 85015853550     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322007     Document Type: Article

References (14)

1. Abramowitz M. and Stegun I.A., Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, Natl. Bur. of Standard, Washington DC, 1964.
2. Al-Musallam F. and Vu Kim Tuan, A class of convolution transformations (submitted).
3. Bochner S. and Chandrasekharan K., Fourier Transforms, Princeton Univ. Press, Princeton, 1949.
4. Churchill R.V., Operational Mathematics, 3rd ed., McGraw-Hill, New York, 1972.
5. Glaeske H.J. and Vu Kim Tuan, Convolution of Hilbert transform and its application to some nonlinear singular equations. Integral Transforms and Special Functions 3(1995), no. 4, p. 263–268.
6. Nguyen Xuan Thao, Kakichev V.A., and Vu Kim Tuan, On the generalized convolutions for Fourier cosine and sine transforms. East-West J. Math. 1(1998), no. 1, p. 85–90.
7. Saigo M. and Yakubovich S.B., On the theory of convolution integrals for G-transforms. Fukuoka Univ. Sci. Reports 21(1991), no. 2, p. 181–193.
8. Srivastava H.M. and Vu Kim Tuan, A new convolution theorem for the Stieltjes transform and its application to a class of singular integral equations. Arch. Math. 64(1995), no. 2, p. 144–149.
9. Sneddon I.N., The Use of Integral Transforms. McGraw-Hill, New York, 1972.
10. Stein E.M. and Weiss G., Introduction to Fourier Analysis on Euclidean Space. Princeton Univ. Press, Princeton, 1991.
11. Titchmarsh E.C., Introduction to the Theory of Fourier Integrals, 2nd ed., Clarendon Press, Oxford, 1967.
12. Watson G.N., A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1944.
13. Vu Kim Tuan and Saigo M., Convolution of Hankel transform and its application to an interal involving Bessel function of first kind. Internat. J. Math. Math. Sci. 18(1995), no. 3, p. 545–550.
14. Vu Kim Tuan, Integral transforms of Fourier cosine convolution type. J. Math. Anal. Appl. 229(1999), p. 519–529.