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Schrödinger operators with singular magnetic vector potentials

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References

  1. Gagliardo, E.: Proprietà di alcune classi di funzione in più variabili. Ricerche di Mat.7, 102–137 (1958)

    Google Scholar 

  2. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Grundlehren der mathematischen Wissenschaften 224. Berlin, Heidelberg, New York, Springer 1977

    Google Scholar 

  3. Ikebe, T., Kato, T.: Uniqueness of self-adjoint extensions of singular elliptic differential operators. Arch. Rational Mech. Anal.9, 77–92 (1962)

    Google Scholar 

  4. Jörgens, K.: Über das wesentliche Spektrum elliptischer Differentialoperatoren vom Schrödinger-Typ. Tech. Report, Univ. of Heidelberg 1965

  5. Kato, T.: Remarks on Schrödinger operators with vector potentials. Integral Equations Operator Theory1, 103–113 (1978)

    Google Scholar 

  6. Kato, T.: Perturbation Theory for Linear Operators. Berlin, Heidelber, New York: Springer 1966

    Google Scholar 

  7. Kato, T.: Schrödinger operator with singular potentials. Israel J. Math.13, 135–148 (1972)

    Google Scholar 

  8. Kato, T.: A second look at the essential selfadjointness of Schrödinger operators. Physical Reality and Mathematical Description, pp. 193–201. D. Reidel Publ. Co., Dordrecht 1974

    Google Scholar 

  9. Marcus, M., Mizel, V.J.: Complete characterization of functions which act, via superposition, on Sobolev spaces. Trans. Amer. Math. Soc.251, 187–218 (1979)

    Google Scholar 

  10. Marcus, M., Mizel, V.J.: Every superposition operator mapping one Sobolev space into another is continuous. J. Funct. Anal.33, 217–229 (1979)

    Google Scholar 

  11. Nirenberg, L.: Remarks on strongly elliptic partial differential equations. Comm. Pure Appl. Math.8, 648–674 (1955)

    Google Scholar 

  12. Perelmuter, M.A., Semenov, Yu.A.: Selfadjointness of elliptic operators with finite or infinite variables. Funktional Anal. i. Prilozen14, 81–82 (1980)

    Google Scholar 

  13. Reed, M., Simon, B.: Methods of Modern Mathematical Physics, II, Fourier Analysis, Self-Adjointness. New York, San Francisco, London: Academic Press 1975

    Google Scholar 

  14. Schechter, M.: Spectra of Partial Differential Operators. Amsterdam, London: North Holland 1971

    Google Scholar 

  15. Schechter, M.: Essential self-adjointness of the Chrödinger operator with magnetic vector potential. J. Func. Anal.20, 93–104 (1975)

    Google Scholar 

  16. Simader, C.G.: Bemerkungen über Schrödinger-Operatoren mit stark singulären Potentialen. Math. Z.138, 53–70 (1974)

    Google Scholar 

  17. Simader, C.G.: Remarks on Kato's inequality. To appear

  18. Simon, B.: Schrödinger Operators with singular magnetic vector potentials. Math. Z.131, 361–370 (1973)

    Google Scholar 

  19. Simon, B.: Maximal and minimal Schrödinger forms. Journal of Operator Theory.1, 37–47 (1979)

    Google Scholar 

  20. Wienholtz, E.: Halbbeschränkte partielle Differentialoperatoren zweiter Ordnung vom elliptischen Typus. Math. Ann.135, 50–80 (1958)

    Google Scholar 

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  1. Fakultät für Mathematik und Physik, Universität Bayreuth, Postfach 3008, D-8580, Bayreuth, Germany

    Herbert Leinfelder & Christian G. Simader

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  1. Herbert Leinfelder
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  2. Christian G. Simader
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Dedicated to our teacher Ernst Wienholtz on his 50th birthday

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Leinfelder, H., Simader, C.G. Schrödinger operators with singular magnetic vector potentials. Math Z 176, 1–19 (1981). https://doi.org/10.1007/BF01258900

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