Mathematische Annalen

, Volume 126, Issue 1, pp 253–262 | Cite as

On some approximate methods concerning the operatorsT* T

  • Tosio Kato


Approximate Method 
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  1. [1]
    Courant, R., undHilbert, D.: Methoden der Mathematischen Physik, I, 2. Aufl., Berlin 1931, pp. 199–209.Google Scholar
  2. [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. [3]
    Friedrichs, K.: Ein Verfahren der Variationsrechnung, Göttinger Nachr. 1929, 13–20.Google Scholar
  4. [4]
    Friedrichs, K.: On differential operators in Hilbert spaces, Amer. J. Math.61. 523–544 (1939).Google Scholar
  5. [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. [6]
    Kato, T.: On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan4, 334–339 (1949).Google Scholar
  7. [7]
    Kato, T.: Perturbation theory of semi-bounded operators, Math. Ann.125, 435–447 (1953).Google Scholar
  8. [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. [9]
    Neumann, J. von: Über adjungierte Funktionaloperatoren, Ann. of Math.33, 294–310 (1932).Google Scholar
  10. [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. [11]
    Trefftz, E.: Konvergenz und Fehlerschätzung beimRitzschen Verfahren, Math. Ann.100, 503–521 (1928).Google Scholar
  12. [12]
    Weyl, H.: The method of orthogonal projection in potential theory, Duke Math. J.7, 411–444 (1940).Google Scholar

Copyright information

© Springer-Verlag 1953

Authors and Affiliations

  • Tosio Kato
    • 1
  1. 1.Tokyo

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