Geodesic
On the spectrum of an integral operator
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 5-9

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

The integral operator which we will consider in this paper is the operator T denned for suitably restricted functions f on (0, ∞) bywhere x >0 and the integral is taken in the Cauchy principal value sense at t = x. This operator plays a considerable role in Wiener–Hopf theory; see [2; Chapter 5].Since T is clearly the restriction to (0, ∞) of minus the Hilbert transformation applied to functions which vanish on (−∞, 0), it follows easily from the theory of the Hilbert transformation, as given in say [6; Theorem 101], that T is a bounded operator from Lp(0, ∞) to itself for 1 < p < ∞. 
Rooney, P. G. On the spectrum of an integral operator. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 5-9. doi: 10.1017/S001708950000625X
@article{10_1017_S001708950000625X,
     author = {Rooney, P. G.},
     title = {On the spectrum of an integral operator},
     journal = {Glasgow mathematical journal},
     pages = {5--9},
     year = {1986},
     volume = {28},
     number = {1},
     doi = {10.1017/S001708950000625X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950000625X/}
}
TY  - JOUR
AU  - Rooney, P. G.
TI  - On the spectrum of an integral operator
JO  - Glasgow mathematical journal
PY  - 1986
SP  - 5
EP  - 9
VL  - 28
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708950000625X/
DO  - 10.1017/S001708950000625X
ID  - 10_1017_S001708950000625X
ER  - 
%0 Journal Article
%A Rooney, P. G.
%T On the spectrum of an integral operator
%J Glasgow mathematical journal
%D 1986
%P 5-9
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708950000625X/
%R 10.1017/S001708950000625X
%F 10_1017_S001708950000625X

[1] 1.Pace, C. Del and Venturi, A., A Wiener–Hopf equation with singular kernel, Matematiche (Catania) 33 (1978), no. 2, 333–347 (1981). Google Scholar

[2] 2.Hochstadt, Harry, Integral equations, (Wiley, 1973). Google Scholar

[3] 3.Koppelman, W. and Pincus, J. D., Spectral representations for finite Hilbert transformations, Math. Z. 71 (1959), 399–407. Google Scholar | DOI

[4] 4.Rooney, P. G., On the and ℋ transformations, Canad. J. Math. 32 (1980), 1021–1044. Google Scholar | DOI

[5] 5.Rooney, P. G., Multipliers for the Mellin transformation, Canad. Math. Bull. 25 (1982), 257–262. Google Scholar | DOI

[6] 6.Titchmarsh, E. C., Theory of Fourier integrals, (Oxford, 1948). Google Scholar

[7] 7.Widom, Harold, Singular integrals in L, Trans. Amer. Math. Soc. 97 (1960), 939–960. Google Scholar | DOI

Cité par Sources :