Abstract
Criteria are established for the unitary equivalence of bounded linear operators to B-Carleman and bi-Carleman integral operators.
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T. Carleman, Sur les equations intégrales singulières a noyau réel et symètrique, Uppsala, Lundequis (1923).
N. I. Akhiezer, “Integral operators with Carleman kernels,” Usp. Matem. Nauk,2, No. 5, 93–132 (1947).
N. I. Akhiezer and I. M. Glazman, The Theory of Linear Operators in Hubert Space [in Russian], Nauka, Moscow (1966).
M. Schreiber and G. Targonski, “Carleman and semi-Carleman operators,” Proc. Amer. Math. Soc.,24, No. 2, 293–299 (1970).
J. Neumann, “Charakterisierung des Spektrums eines Integraloperators,” Collected Works, 4, Pergamon Press, Oxford-London-New York-Paris (1962), pp. 38–55.
B. Misra, D. Speiser, and G. Targonski, “Integral operators in the theory of scattering,” Helv. Phys. Acta.,36, No. 7, 963–980 (1963).
V. B. Korotkov, “The classification and characteristic properties of Carleman operators,” Dokl. Akad. Nauk SSSR,190, No. 6, 1274–1277 (1970).
J. Weidmann, “Carlemanoperatoren,” Manuscripta Math.,2, No. 1, 1–38 (1970).
V. B. Korotkov, “On integral operators,” Dokl. Akad. Nauk SSSR,195, No. 6, 1267–1269 (1970).
V. B. Korotkov, “On integral operators with Carleman kernels,” Dokl. Akad. Nauk SSSR,165, No. 4, 748–751 (1965).
V. B. Korotkov, “On a problem of D. Targonskii on the relation between the kernel of a normal Carleman operator and the kernel of an adjoint operator,” Matem. Zametki,6, No. 5, 599–606 (1969).
S. Kaczmarz and H. Steinhaus, The Theory of Orthogonal Series, Chelsea Pub., New York.
I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Non-Self-Adjoint Operators [in Russian], Nauka, Moscow (1965).
N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).
V. B. Korotkov, “On the characteristic properties of integral operators with kernels of Carleman type,” Sibirsk. Matem. Zh.,11, No. 1, 103–127 (1970).
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Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 601–610, April, 1976.
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Korotkov, V.B. The unitary equivalence of linear operatops to integral operators. Mathematical Notes of the Academy of Sciences of the USSR 19, 364–368 (1976). https://doi.org/10.1007/BF01156799
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DOI: https://doi.org/10.1007/BF01156799