Literature Cited
P. Halmos, Measure Theory, D. Van Nostrand, New York (1950).
T. Carleman, Sur les Equations Integrales Singulieres à Noyau et Symetrique, Uppsala (1923).
N. I. Akhieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum, Akademie Verlag, Berlin (1968).
M. Schreiber, “Semi-Carleman operators,” Acta Sci. Math.,24, No. 1-2 82–87 (1963).
B. Misra, D. Speiser, and G. Targonski “Integral operators in the theory of scattering,” Helv. Phys. Acta,36, No. 7, 963–980 (1963).
N. I. Akhiezer, “Integral operators with Carleman kernels,” Usp. Matem. Nauk,2, No. 5, 93–132 (1947).
V. B. Korotkov, “Classification and characteristic properties of Carleman operators,” Dokl. Akad. Nauk SSSR,190, No. 6, 1274–1277 (1970).
R. Phillips, “On weakly compact subsets of a Banach space,” Amer. J. Math.,65, 108–136 (1943).
V. I. Rybakov, “On vector measures,” Izv. Vuzov. Matem.,12, 92–101 (1968).
E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Coll. Publ., Vol. 31, New York (1957).
V. B. Korotkov, “On integral operators with Carleman kernels,” Dokl. Akad. Nauk SSSR,165, No. 4 748–751 (1965).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No. 5, pp. 1041–1055, September–October, 1971.
Rights and permissions
About this article
Cite this article
Korotkov, V.B. Integral operators with kernels satisfying Carleman and Akhiezer conditions. Sib Math J 12, 750–760 (1971). https://doi.org/10.1007/BF00966512
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00966512