Skip to main content
Log in

Complex geometry and operator theory

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Bergman, S.,The Kernel Function and Conformal Mapping. Math. Surveys No. 5, Amer. Math. Soc., Providence, R.I., 1950.

    MATH  Google Scholar 

  2. Calabi, E., Isometric imbedding of complex manifolds.Ann. of Math., (2) 58 (1953) 1–23.

    Article  MathSciNet  Google Scholar 

  3. Chern, S. S., Holomorphic curves in the plane, inDifferential Geometry, in honor of K. Yano, Kinokuniya, Tokyo, 1972, 73–94.

    Google Scholar 

  4. Clary, W. S., Quasi-similarity and subnormal operators, Thesis, University of Michigan, 1973.

  5. Cowen, M. J. &Douglas, R. G., Complex geometry and operator theory.Bull. Amer. Math. Soc., 83 (1977), 131–133.

    Article  MathSciNet  MATH  Google Scholar 

  6. — Operator theory and complex geometry, Proc. Sympos. Pure Math., vol. 30, part 2, Amer. Math. Soc., Providence, R.I., 229–236, 1977.

    Google Scholar 

  7. Cowen, M. &Griffiths, P., Holomorphic curves and metrics of negative curvature.J. d'Analyse Math., 29 (1976), 93–153.

    Article  MathSciNet  MATH  Google Scholar 

  8. Douglas, R. G.,Banach Algebra Techniques in Operator Theory. Academic Press, New York, 1972.

    MATH  Google Scholar 

  9. Flanders, H.,Differential Forms with Applications to the Physical Sciences. Academic Press, New York, 1963.

    MATH  Google Scholar 

  10. Gamelin, T. W.,Uniform Algebras. Prentice Hall, Englewood Cliffs, N. J., 1969.

    MATH  Google Scholar 

  11. Golubitsky, M. &Guillemin, V.,Stable Mappings and Their Singularities, Springer-Verlag, New York, 1973.

    MATH  Google Scholar 

  12. Grauert, H., Analytische Faserungen über holomorph vollstandigen Räumen.Math. Ann., 135 (1958), 263–273.

    Article  MathSciNet  MATH  Google Scholar 

  13. Griffiths, P. A., On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry.Duke Math. J., 41 (1974), 775–814.

    Article  MathSciNet  MATH  Google Scholar 

  14. Entire Holomorphic. Mappings in One and Several Complex Variables. Princeton University Press, Princeton, 1976.

    MATH  Google Scholar 

  15. Halmos, P. R.,A Hilbert Space Problem Book, Van Nostrand, Princeton, 1967.

    MATH  Google Scholar 

  16. Kuranishi, M., On E. Cartan's prolongation theory of exterior differential systems.Amer. J. Math., 79 (1957), 1–47.

    Article  MathSciNet  MATH  Google Scholar 

  17. Nomizu, K., Characteristic roots and vectors of a differentiable family of symmetric matrices,Linear and Multilinear Algebra, 1 (1973), 159–162.

    MathSciNet  Google Scholar 

  18. Pearcy, C., A complete set of unitary invariants for operators generating finiteW*-algebras of type I.Pacific J. Math., 12 (1962), 1405–1416.

    MathSciNet  MATH  Google Scholar 

  19. Shapiro, H. S. &Shields, A. L., On the zeros of functions with finite Dirichlet integral and some related function spaces.Math. Z., 80 (1962), 217–229.

    Article  MathSciNet  MATH  Google Scholar 

  20. Shields, A. L., Weighted shift operators and analytic function theory, pp. 51–128.Topics in Operator Theory, Ed. C. Pearcy, Math. Surveys No. 13, Amer. Math. Soc., Providence, R. I. 1974.

    Google Scholar 

  21. Specht, W., Zur Theorie der Matrizen II.Iber. Deutsch. Math. Verein., 50 (1940), 19–23.

    MathSciNet  MATH  Google Scholar 

  22. Šubin, M. A., Factorization of parameter-dependent matrix functions in normal rings and certain related questions in the theory of Noetherian operators.Mat. Sb., 73 (113) (1967) 610–629;Math. USSR Sb., 2 (1967), 543–560.

    MathSciNet  Google Scholar 

  23. Taylor, G. D., Multipliers onD α*.Trans. Amer. Math. Soc., 123 (1966), 229–240.

    Article  MathSciNet  MATH  Google Scholar 

  24. Taylor, J. L., A joint spectrum for several commuting operators.J. Functional Anal., 6 (1970), 172–191.

    Article  MATH  Google Scholar 

  25. Veblen, O.,Invariants of Quadratic Differential Forms. Cambridge University Press, 1927.

  26. Wells, R. O.,Differential Analysis on Complex Manifolds. Prentice Hall, Englewood Cliffs, N. J., 1973.

    MATH  Google Scholar 

  27. Wu, H.,The Equidistribution Theory of Holomorphic Curves, Princeton University Press, Princeton, 1970.

    MATH  Google Scholar 

  28. Kato, T.,Perturbation Theory of Linear Operators. Springer-Verlag, New York, 1966.

    Google Scholar 

  29. Hörmander, L.,An Introduction to Complex Analysis in Several Variables. Van Nostrand, Princeton, 1966.

    MATH  Google Scholar 

  30. Cornalba, M. &Griffiths, P., Analytic Cycles and Vector Bundles on Non-compact Algebraic Varieties.Inv. Math., 28 (1975), 1–106.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to M. G. Krein

Research supported in part by grants from the National Science Foundation and the Research Foundation of the State of New York.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cowen, M.J., Douglas, R.G. Complex geometry and operator theory. Acta Math. 141, 187–261 (1978). https://doi.org/10.1007/BF02545748

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02545748

Keywords

Navigation