On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality

Integral Equations and Operator Theory

Volumn 36, Issue 3, 2000, Pages 288-324

  Johnsen, Jon ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038041007     PISSN: 0378620X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01213926     Document Type: Article

References (28)

1. S. Agmon, Lectures on exponential decay of solutions of second order elliptic equations, Math. Notes, vol. 29, Princeton University Press, 1978.
2. P. Bolley, M. Dauge, and B. Helffer, Conditions suffisantes pour l'injection compacte d'espaces de Sobolev à poids, Séminaire équation aux dérivées partielles (France), vol. 1, Université de Nantes, France, 1989, pp. 1-14.
3. V. Bach, T. Jecko, and J. Sjöstrand, Correlation asymptotics of classical lattice spin systems with nonconvex Hamilton function at low temperature, 1998, (in preparation, 4 August).
4. H. J. Brascamp and E. H. Lieb, On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems including inequalities for log concave functions, and with applications to the diffusion equation, J. Funct. Analysis 22 (1976), 366-389.
5. J. Brüning and M. Lesch, Hilbert complexes, J. Funct. Analysis 108 (1992), 88-132.
6. G. de Rham, Variétes différentiables, Hermann, Paris, 1955.
7. Helffer, B., Spectral properties of the Kac operator in large dimension, Proceedings on mathematical quantum theory II: Schrödinger operators (Providence, R. I.) (Feldman, J. and Froese, R. and Rosen, L. M., ed.), CMR proceedings and lecture notes, vol. 8, A. M. S., Providence, R. I., 1995, Proc. of the Canadian Math. Soc. annual sem. on math, quantum theory; Vancouver, August 1993.
8. B. Helffer, Remarks on the decay of correlations and Witten Laplacians. Analysis of the dependence on the interaction, September 1997, (accepted by Rev. in Math. Physics).
9. B. Helffer, Remarks on the decay of correlations and Witten Laplacians. Applications to log-Sobolev inequalities, September 1997, (preliminary note).
10. B. Helffer, Remarks on the decay of correlations and Witten Laplacians - the Brascamp-Lieb inequality and semiclassical limit, J. Functional Analysis 155 (1998), 571-586.
11. B. Helffer, Spectral theory and applications, lecture notes, January 1999.
12. L. Hörmander, Introduction to complex analysis in several variables, 3 ed., North-Holland Mathematical Library, vol. 7, Elsevier, Amsterdam, 1966, (1990).
13. L. Hörmander, The analysis of linear partial differential operators, Grundlehren der mathematischen Wissenschaften, vol. 256, 257, 274, 275, Springer Verlag, Berlin, 1983, 1985.
14. B. Helffer and J. Sjöstrand, On the correlation for Kac like models in the convex case, J. Stat. Physics 74 (1994), 349-409, (already in report no. 9, Mittag Leffler Institute, 1992-93).
15. J Jost, Riemannian geometry and geometric analysis, 2. ed., Universitext, Springer, 1998.
16. T. Kato, Schrödinger operators with singular potentials, Israel J. Math. 13 (1973), 135-148.
17. J.-M. Kneib and F. Mignot, Equation de Schmoluchowski généralisée, Ann. Math. Pura Appl.(IV) 167 (1994), 257-298.
18. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Editions Dunod, 1968, Engl. translation"Nonhomogeneous boundary problems and applications", Springer Verlag 1972.
19. A. Naddaf and T. Spencer, On homogenization and scaling limit of gradient perturbations of a massless free field, Comm. Math. Physics 183 (1997), 55-84.
20. A. Persson, Bounds for the discrete parts of the spectrum of a semi-bounded Schrödinger operator, Math. Scand. 8 (1960), 143-153.
21. L. Schwartz, Théorie des distributions a valeurs vectorielles, Ann. Institut Fourier 7-8 (1957 1959) 1-141, 1-209.
22. L. Schwartz, Théorie des distributions, revised and enlarged ed., Hermann, Paris, 1966.
23. C. G. Simader, Essential self-adjointness of Schrödinger operators bounded from below, Math. Z. 159 (1978), 47-50.
24. J. Sjöstrand, Potential wells in high dimensions II, more about the one well case, Ann. Inst Poincaré Sect. Phys. Th. 58 (1993), no. 1, 42-53.
25. J. Sjöstrand, Correlation asymptotics and Witten Laplacians, Algebra and Analysis 8 (1996), no. 1, 160-191, also in St. Petersburg Math. J., 8 (1997), 123-148.
26. J. Sjöstrand, Correlation asymptotics and Witten Laplacians, Algebra and Analysis 8 (1996), no. 1, 160-191, also in St. Petersburg Math. J., 8 (1997), 123-148.
27. d, 1999, (preprint, Université de Paris-Sud, Orsay, France).
28. E. Witten, Supersymmetry and Morse theory, J. Differential Geometry 17 (1982), 661-692.