On Carleman Integral Operators
Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 351-357

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L 2(a, b) 1 with the property 2 were originally defined by T. Carleman [4]. Here he imposed on the kernel the conditions of measurability and hermiticity, 3 for all x with the exception of a countable set with a finite number of limit points and 4 where J δ denotes the interval [a, b] with the exception of subintervals |x - ξv| < δ; here ξv represents a finite set of points for which (3) fails to hold.
Costley, Charles G. On Carleman Integral Operators. Canadian mathematical bulletin, Tome 13 (1970) no. 3, pp. 351-357. doi: 10.4153/CMB-1970-066-3
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     title = {On {Carleman} {Integral} {Operators}},
     journal = {Canadian mathematical bulletin},
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     number = {3},
     doi = {10.4153/CMB-1970-066-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-066-3/}
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