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Spectral properties of some differential and pseudodifferential operators. Applications to some quark models

Спектральные свойст ва некоторых диффере нциальных и псевдо-дифференциал ьпых операторов. Применен ие к некоторым кварко вым моделям

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Il Nuovo Cimento A (1965-1970)

Summary

We prove that some self-adjoint operators, which are the Friedrichs realization in L2 of a class of nonelliptic differential operators, have a positive, discrete spectrum. The results obtained are applied to study operators which occur in the dynamical description of some elementary particles.

Riassunto

Si dimostra che alcuni operatori autoaggiunti, che sono la realizzazione di Friedriohs in L2 di una classe di operatori differenziali non ellittici, hanno spettro positivo e discreto. I risultati ottenuti sono applicati allo studio di operatori che intervengono nella descrizione dinamica di alcune particelle elementari.

Резюме

Мы доказываем, что сам о-сопряженные операторы, которые пр едставляют реализацию Фридрихс а на L2 для класса неэллиптических диф ференциальных операторов, имеют пол ожительный дискретн ый спектр. Полученные результаты применяю тся для исследования операторов, которые появляются в динамическом описан ии некоторых элемент арных частиц.

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Reference

  1. R. P. Feynman, M. Kislinger andF. Ravndal:Phys. Rev.,3, 2706 (1971).

    Article  ADS  Google Scholar 

  2. Y. S. Kim:Phys. Rev. D,14, 273 (1976).

    Article  ADS  Google Scholar 

  3. G. Preparata :Unconventional approach to ≪ quark confinement ≫, inProceedings of the IX Ecole d’Eté de Physique des Particules de Gif-sur-Yvette (1977).

  4. T. Kato:Perturbation Theory for Linear Operators (New York, N. Y., 1966).

  5. V. Benci:J. Diff. Eq.,31, 16 (1979).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. M. Reed and B. Simon:Methods of Modern Mathematical Physics IV (New York, N. Y., 1978).

  7. M. S. Berger andM. Scheciiter:Trans. Am. Math. Soc,172, 261 (1972).

    Article  Google Scholar 

  8. L. Hörmander:Acta. Math.,94, 161 (1955).

    Article  MathSciNet  Google Scholar 

  9. V. Benci andD. Fortunato:J. Math. Anal. Appl.,64, 695 (1978).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Istituto di Matematica Applicata, Via Be David 200, 70125, Bari, Italia

    V. Benci & D. Fortunato

Authors
  1. V. Benci
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  2. D. Fortunato
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Additional information

This research was supported by G.N.A.F.A. of C.N.R.

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Benci, V., Fortunato, D. Spectral properties of some differential and pseudodifferential operators. Applications to some quark models. Nuov Cim A 62, 295–306 (1981). https://doi.org/10.1007/BF02770971

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  • DOI: https://doi.org/10.1007/BF02770971

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