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On some approximate methods concerning the operatorsT* T

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Bibliography

  1. Courant, R., undHilbert, D.: Methoden der Mathematischen Physik, I, 2. Aufl., Berlin 1931, pp. 199–209.

  2. Diaz, J. B., andGreenberg, H. J.: Upper and lower bounds for the solution of the first biharmonic boundary value problem, J. Math. Phys.27, 193–201 (1948).

    Google Scholar 

  3. Friedrichs, K.: Ein Verfahren der Variationsrechnung, Göttinger Nachr. 1929, 13–20.

  4. Friedrichs, K.: On differential operators in Hilbert spaces, Amer. J. Math.61. 523–544 (1939).

    Google Scholar 

  5. Greenberg, H. J.: The determination of upper and lower bounds for the solution of the Dirichlet problem, J. Math. Phys.27, 161–182 (1948).

    Google Scholar 

  6. Kato, T.: On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan4, 334–339 (1949).

    Google Scholar 

  7. Kato, T.: Perturbation theory of semi-bounded operators, Math. Ann.125, 435–447 (1953).

    Google Scholar 

  8. Murray, F. J.: Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations, Trans. Amer. Math. Soc.37, 301–338 (1935).

    Google Scholar 

  9. Neumann, J. von: Über adjungierte Funktionaloperatoren, Ann. of Math.33, 294–310 (1932).

    Google Scholar 

  10. Rayleigh, Lord: On the theory of resonance, Phil. Trans.161, 77–118 (1870); Scientific Papers, Vol. I, pp. 33–75; Theory of Sound, Vol. II, §§ 305–308.

    Google Scholar 

  11. Trefftz, E.: Konvergenz und Fehlerschätzung beimRitzschen Verfahren, Math. Ann.100, 503–521 (1928).

    Google Scholar 

  12. Weyl, H.: The method of orthogonal projection in potential theory, Duke Math. J.7, 411–444 (1940).

    Google Scholar 

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  1. Tokyo

    Tosio Kato

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  1. Tosio Kato
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Kato, T. On some approximate methods concerning the operatorsT* T . Math. Ann. 126, 253–262 (1953). https://doi.org/10.1007/BF01343163

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