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Critères d’auto-adjonction : Rellich, Kato & Friedrichs

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Théorie spectrale et mécanique quantique

Part of the book series: Mathématiques et Applications ((MATHAPPLIC,volume 87))

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Abstract

La théorie des perturbations de Rellich-Kato est présentée, suivi de la théorie de Friedrichs sur les formes quadratiques. Cette dernière permet de construire des extensions auto-adjointes naturelles d’un point de vue physique.

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References

  1. F. V. ATKINSON, On some results of Everitt and Giertz, Proc. R. Soc. Edinb., Sect. A, Math., 71 (1973), pp. 151–158.

    Google Scholar 

  2. R. COURANT AND D. HILBERT, Methods of mathematical physics. Vol. I, 1953.

    Google Scholar 

  3. M. DAUGE, Elliptic boundary value problems on corner domains, vol. 1341 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1988. Smoothness and asymptotics of solutions.

    Google Scholar 

  4. E. B. DAVIES, Some norm bounds and quadratic form inequalities for Schrödinger operators, J. Oper. Theory, 9 (1983), pp. 147–162.

    MATH  Google Scholar 

  5. W. N. EVERITT AND M. GIERTZ, Inequalities and separation for certain ordinary differential operators, Proc. Lond. Math. Soc. (3), 28 (1974), pp. 352–372.

    Google Scholar 

  6. W. N. EVERITT AND M. GIERTZ, Inequalities and separation for Schrödinger type operators in L 2(R n), Proc. Roy. Soc. Edinburgh Sect. A, 79 (1977/78), pp. 257–265.

    Google Scholar 

  7. L. C. EVANS, Partial differential equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, second ed., 2010.

    MATH  Google Scholar 

  8. W. D. EVANS AND A. ZETTL, Dirichlet and separation results for Schrödinger-type operators, Proc. R. Soc. Edinb., Sect. A, Math., 80 (1978), pp. 151–162.

    Google Scholar 

  9. K. FRIEDRICHS, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren. I, II, Math. Ann., 109 (1934), pp. 465–487, 685–713.

    Article  MathSciNet  Google Scholar 

  10. M. J. GANDER AND F. KWOK, Chladni figures and the Tacoma Bridge: motivating PDE eigenvalue problems via vibrating plates, SIAM Rev., 54 (2012), pp. 573–596.

    Google Scholar 

  11. P. GRISVARD, Elliptic problems in nonsmooth domains, vol. 24 of Monographs and Studies in Mathematics, Pitman (Advanced Publishing Program), Boston, MA, 1985.

    Google Scholar 

  12. D. HAHN AND M. ÖZISIK, Heat Conduction, Wiley, 2012.

    Google Scholar 

  13. T. KATO, Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc., 70 (1951), pp. 195–221.

    MathSciNet  MATH  Google Scholar 

  14. P. D. LAX AND A. N. MILGRAM, Parabolic equations, Ann. Math. Stud., 33 (1954), pp. 167–190.

    Google Scholar 

  15. N. OKAZAWA, On the perturbation of linear operators in Banach and Hilbert spaces, J. Math. Soc. Japan, 34 (1982), pp. 677–701.

    Article  MathSciNet  Google Scholar 

  16. F. RELLICH, Störungstheorie der Spektralzerlegung. IV., Math. Ann., 116 (1937), pp. 555–570.

    Article  MathSciNet  Google Scholar 

  17. ——, Methods of Modern Mathematical Physics. II. Fourier analysis, self-adjointness, Academic Press, New York, 1975.

    Google Scholar 

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Lewin, M. (2022). Critères d’auto-adjonction : Rellich, Kato & Friedrichs. In: Théorie spectrale et mécanique quantique. Mathématiques et Applications, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-030-93436-1_3

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