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On Fredholm operators and the essential spectrum of singular integral operators

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Bibliography

  1. Atkinson, F. V.: The normal solvability of linear equations in normed spaces. Mat. Sbornik28 (70), 3–14 (1951), (Russian).

    Google Scholar 

  2. Browder, F. E.: On the spectral theory of elliptic differential operators. I. Math. Ann.142, 22–130 (1961).

    Google Scholar 

  3. Calderón, A. P., and A. Zygmund: On the existence of certain singular integrals. Acta Math.88, 85–139 (1952).

    Google Scholar 

  4. Deprit, A.: Contribution à l'étude de l'algèbre des applications linéaires continues d'un espace localement convexe séparé. Publication de la Académie Royale de Belgique, No. 1692 (1959).

  5. Devinatz, A., and I. I. Hirschman Jr: The spectra of multiplier transforms onl p. American J. of Math.80, 829–842 (1958).

    Google Scholar 

  6. Gokhberg, I. C.: On an application of the theory of normed rings to singular integral equations. Uspehi Mat. Nauk7, 2 (48), 149–156 (1952), (Russian).

    Google Scholar 

  7. —— On linear equations in normed spaces. Dokl. Akad. Nauk SSSR76, 477–480 (1951), (Russian).

    Google Scholar 

  8. ——, and M. G. Krein: The basic propositions on defect numbers, root numbers, and indices of linear operators. Uspehi Mat. Nauk12, 2 (74), 43–118 (1957), (Russian). Am. Math. Soc. Transl., Series 2, Vol.13.

    Google Scholar 

  9. Goldberg, S.: Unbounded linear operators. Theory and applications. New York: McGraw Hill 1966.

    Google Scholar 

  10. Halmos, P. R.: A Hilbert space problem book. Princeton: D. van Nostrand 1967.

    Google Scholar 

  11. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  12. Mikhlin, S. G.: Multidimensional singular integrals and integral equations. Moscow: Fizmatiz 1962 (Russian). English edition: New York: Pergamon Press 1965.

    Google Scholar 

  13. Nieto, J.: Variations on a theme by Mikhlin. Math. Ann.162, 331–336 (1966).

    Google Scholar 

  14. Nikolsky, S. M.: Linear equations in normed spaces. Izv. Akad. Nauk SSSR Ser. Mat.,7, No. 3, 147–163 (1943), (Russian).

    Google Scholar 

  15. Schechter, M.: Fredholm operators and the essential spectrum. (Report), Courant Inst. of Math. Sciences, N.Y.U. (1965).

  16. —— On the essential spectrum of an arbitrary operator, I. J. Math. Anal. and Appl.13, 205–215 (1966).

    Google Scholar 

  17. Seeley, R. T.: The index of elliptic systems of singular integral operators. J. Math. Anal. and Appl.7, 289–309 (1963).

    Google Scholar 

  18. Wolf, F.: On the invariance of the essential spectrum under a change of boundary conditions of partial differential operators. Indag. Math.21, 142–147 (1959).

    Google Scholar 

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Nieto, J.I. On Fredholm operators and the essential spectrum of singular integral operators. Math. Ann. 178, 62–77 (1968). https://doi.org/10.1007/BF01350625

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