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The heat equation for the\(\bar \partial - Neumann\) problem in a strictly pseudoconvex Siegel domainproblem in a strictly pseudoconvex Siegel domain

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References

  1. S. S. Chern and J. K. Moser,Real hypersurfaces in complex manifolds, Acta Math.133 (1974). 219–271.

    Article  MathSciNet  Google Scholar 

  2. G. B. Folland,Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat.13 (1975), 161–207.

    Article  MATH  MathSciNet  Google Scholar 

  3. G. B. Folland and J. J. Kohn,The Neumann Problem for the Cauchy-Riemann Complex, Ann. of Math. Studies75, Princeton University Press, Princeton, New Jersey, 1972.

    MATH  Google Scholar 

  4. G. B. Folland and E. M. Stein, Estimates for the\(\bar \partial _b \) complex and analysis on the Heisenberg group, Comm. Pure. Appl. Math.27 (1974), 429–522.

    Article  MATH  MathSciNet  Google Scholar 

  5. B. Gaveau,Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents. Acta. Math.139 (1977), 95–153.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. C. Greiner,An asymptotic expansion for the heat equation, Arch. Rational Mech. Anal.41 (1971), 163–218.

    Article  MATH  MathSciNet  Google Scholar 

  7. P. C. Greiner and E. M. Stein, Estimates for the\(\bar \partial - Neumann\) Problem, Mathematical Notes19, Princeton University Press, Princeton, New Jersey, 1977.

    MATH  Google Scholar 

  8. A. Hulanicki,The distribution of energy in the Brownian motion in the Gaussian field and analytic-hypoellipticity of certain subelliptic operators on the Heisenberg group, Studia Math.56 (1976), 165–173.

    MATH  MathSciNet  Google Scholar 

  9. M. Kac,Can one heart the shape of a drum?, Amer. Math. Monthly73 (April, 1966), 1–23.

    Article  Google Scholar 

  10. O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva,Linear and Quasilinear Equations of Parabolic Type, Translations of Math. Monographs,23, Amer. Math. Soc. Providence. Rhode Island, 1968.

    Google Scholar 

  11. H. P. McKean and I. M. Singer,Curvature and the eigenvalues of the Laplacian: J. Differential Geometry1 (1967), 43–69.

    MATH  MathSciNet  Google Scholar 

  12. D. H. Phong,On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A.76 (1979), 1554–1558.

    Article  MATH  MathSciNet  Google Scholar 

  13. F. Riesz and B. Sz.-Nagy,Functional Analysis, Frederick Ungar Publishing Co., New York, 1955.

    Google Scholar 

  14. N. Wiener,The Fourier Integral and Certain of its Applications, Dover Publications,Inc., New York, 1951.

    Google Scholar 

  15. K. Yosida,Functional Analysis, 4th. edn., Springer-Verlag, Berlin, 1974.

    MATH  Google Scholar 

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  1. Department of Mathematics, Columbia University, 10027, New York, NY, USA

    Nancy K. Stanton

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  1. Nancy K. Stanton
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Stanton, N.K. The heat equation for the\(\bar \partial - Neumann\) problem in a strictly pseudoconvex Siegel domainproblem in a strictly pseudoconvex Siegel domain. J. Anal. Math. 38, 67–112 (1980). https://doi.org/10.1007/BF03033878

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  • DOI: https://doi.org/10.1007/BF03033878

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