On delta-extension for a Noether operator (Q2066427)

In the context of linear Fredholm integral equations of the third kind, several authors studied the problem of the construction of solutions in the class of generalized functions (see, e.g., [\textit{J. H. Ferziger} and \textit{H. G. Kaper}, Mathematical theory of transport processes in gases. Amsterdam-London: North-Holland Publ. Company (1972); \textit{D. Hilbert}, Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. Reprint. New York: Chelsea Co. (1953; Zbl 0050.10201); \textit{E. Picard}, C. R. Acad. Sci., Paris 150, 489--491 (1910; JFM 41.0387.02); \textit{G. R. Bart}, J. Math. Anal. Appl. 79, 48--57 (1981; Zbl 0452.45001); \textit{G. R. Bart} and \textit{R. L. Warnock}, SIAM J. Math. Anal. 4, 609--622 (1973; Zbl 0265.45001); \textit{N. Sukavanam}, J. Math. Anal. Appl. 100, 478--485 (1984; Zbl 0568.45001)]). Some preliminaries about Noether operators and integral equations of the third kind are presented in Section 2. Then the authors define in Section 3 the fundamental spaces and associated operators, along with their basic properties, to tackle the problem. In Section 4, they carefully investigate the Noether property of the operator defined in Equation (3).