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The unitary equivalence of linear operatops to integral operators

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Abstract

Criteria are established for the unitary equivalence of bounded linear operators to B-Carleman and bi-Carleman integral operators.

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Literature cited

  1. T. Carleman, Sur les equations intégrales singulières a noyau réel et symètrique, Uppsala, Lundequis (1923).

    Google Scholar 

  2. N. I. Akhiezer, “Integral operators with Carleman kernels,” Usp. Matem. Nauk,2, No. 5, 93–132 (1947).

    Google Scholar 

  3. N. I. Akhiezer and I. M. Glazman, The Theory of Linear Operators in Hubert Space [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  4. M. Schreiber and G. Targonski, “Carleman and semi-Carleman operators,” Proc. Amer. Math. Soc.,24, No. 2, 293–299 (1970).

    Google Scholar 

  5. J. Neumann, “Charakterisierung des Spektrums eines Integraloperators,” Collected Works, 4, Pergamon Press, Oxford-London-New York-Paris (1962), pp. 38–55.

    Google Scholar 

  6. B. Misra, D. Speiser, and G. Targonski, “Integral operators in the theory of scattering,” Helv. Phys. Acta.,36, No. 7, 963–980 (1963).

    Google Scholar 

  7. V. B. Korotkov, “The classification and characteristic properties of Carleman operators,” Dokl. Akad. Nauk SSSR,190, No. 6, 1274–1277 (1970).

    Google Scholar 

  8. J. Weidmann, “Carlemanoperatoren,” Manuscripta Math.,2, No. 1, 1–38 (1970).

    Google Scholar 

  9. V. B. Korotkov, “On integral operators,” Dokl. Akad. Nauk SSSR,195, No. 6, 1267–1269 (1970).

    Google Scholar 

  10. V. B. Korotkov, “On integral operators with Carleman kernels,” Dokl. Akad. Nauk SSSR,165, No. 4, 748–751 (1965).

    Google Scholar 

  11. 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).

    Google Scholar 

  12. S. Kaczmarz and H. Steinhaus, The Theory of Orthogonal Series, Chelsea Pub., New York.

  13. I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Non-Self-Adjoint Operators [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  14. N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).

    Google Scholar 

  15. V. B. Korotkov, “On the characteristic properties of integral operators with kernels of Carleman type,” Sibirsk. Matem. Zh.,11, No. 1, 103–127 (1970).

    Google Scholar 

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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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