The solution of dual series and dual integral equations
Glasgow mathematical journal, Tome 6 (1964) no. 3, pp. 123-129

Voir la notice de l'article provenant de la source Cambridge University Press

There exist several different approaches to the problem of solving dual integral equations involving Bessel Functions [1, 2, 3, 4, 5, 6,7], and Erdelyi and Sneddon in a recent paper [8] have shown that the introduction of certain operators occurring in the theory of fractional integration enables the relationships between the various methods to be clearly demonstrated. For dual integral equations other than those involving Bessel Functions the operators introduced by Erdélyi and Sneddon are not always the appropriate ones to use and it seems to be of interest to consider this more general type of situation.
Williams, W. E. The solution of dual series and dual integral equations. Glasgow mathematical journal, Tome 6 (1964) no. 3, pp. 123-129. doi: 10.1017/S2040618500034870
@article{10_1017_S2040618500034870,
     author = {Williams, W. E.},
     title = {The solution of dual series and dual integral equations},
     journal = {Glasgow mathematical journal},
     pages = {123--129},
     year = {1964},
     volume = {6},
     number = {3},
     doi = {10.1017/S2040618500034870},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034870/}
}
TY  - JOUR
AU  - Williams, W. E.
TI  - The solution of dual series and dual integral equations
JO  - Glasgow mathematical journal
PY  - 1964
SP  - 123
EP  - 129
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034870/
DO  - 10.1017/S2040618500034870
ID  - 10_1017_S2040618500034870
ER  - 
%0 Journal Article
%A Williams, W. E.
%T The solution of dual series and dual integral equations
%J Glasgow mathematical journal
%D 1964
%P 123-129
%V 6
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034870/
%R 10.1017/S2040618500034870
%F 10_1017_S2040618500034870

[1] 1.Titchmarsh, E. C., Theory of Fourier integrals (Oxford, 1937), p. 334. Google Scholar

[2] 2.Busbridge, I. W., Dual integral equations, Proc. London Math. Soc. 44 (1938), 115–129. Google Scholar

[3] 3.Gordon, A. N., Dual integral equations, J. London Math. Soc. 29 (1954), 360–363. Google Scholar | DOI

[4] 4.Copson, E. T., On certain dual integral equations, Proc. Glasgow Math. Assoc. 5 (1961), 21–24. Google Scholar | DOI

[5] 5.Sneddon, I. N., The elementary solution of dual integral equations, Proc. Glasgow Math. Assoc. 4 (1960), 108–110. Google Scholar | DOI

[6] 6.Noble, B., Certain dual integral equations, J. Math. Phys. 37 (1955), 128–136. Google Scholar | DOI

[7] 7.Williams, W. E., Solution of certain dual integral equations, Proc. Edinburgh Math. Soc. 12 (1961), 213–216. Google Scholar | DOI

[8] 8.Erdélyi, A. and Sneddon, I. N., Fractional integration and dual integral equations, Canad. J. Math. 14 (1962), 685–693. Google Scholar

[9] 9.Copson, E. T., On the problem of the electrified disc, Proc. Edinburgh Math. Soc. 8 (1947), 14–19. Google Scholar | DOI

[10] 10.Tranter, C. J., Dual trigonometrical series, Proc. Glasgow Math. Assoc. 4 (1960), 49–57. Google Scholar | DOI

[11] 11.Collins, W. D., On some dual series equations and their applications to electrostatic problems for spheroidal caps, Proc. Cambridge Philos. Soc. 57 (1961), 367–384. Google Scholar | DOI

[12] 12.Noble, B., Wiener-Hopf methods (Oxford, 1958), p. 230. Google Scholar

[13] 13.Williams, W. E., A class of mixed boundary value problems, J. Math. Mech. 11 (1962), 109–120. Google Scholar

[14] 14.Williams, W. E., Diffraction by a disk, Proc. Roy. Soc. Ser. A 267 (1962), 77–87. Google Scholar

[15] 15.Williams, W. E., A class of integral equations, Proc. Cambridge Philos. Soc. 59 (1963), 589–597. Google Scholar | DOI

[16] 16.Tranter, C. J., On some dual integral equations, Quart. J. Math. Oxford Ser. (2) 2 (1951), 60–66. Google Scholar | DOI

[17] 17.Jones, D. S., A new method for calculating scattering with particular reference to the circular disk, Comm. Pure Appl. Math. 9 (1956), 713–746. Google Scholar

[18] 18.Sneddon, I. N., Fractional integration and dual integral equations (North Carolina State College, 06 1962). Google Scholar

Cité par Sources :