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Department of Mathematics

Louis de Branges de Bourcia

Louis de Branges de Bourcia Distinguished Professor Emeritus of Mathematics
  • 765-49-67330
  • MATH 448
branges@purdue.edu
Research Interest(s):
complex analysis, Fourier analysis, functional analysis

Currently available papers are:

Research Proposal (in pdf format)

The Riemann Hypothesis

The Banach measure problem

Invariant subspaces

Hilbert Spaces of Entire Functions

Faculty Directory

Staff Directory

Publications listed in MathSciNet

  1. Louis de Branges. Quantization of the gamma function. In Approximation and computation (West Lafayette, IN, 1993), volume 119 of Internat. Ser. Numer. Math., pages 23-28. Birkhäuser Boston, Boston, MA, 1994.
  2. 1994 Steele Prizes. Notices Amer. Math. Soc., 41(8):905-912, 1994.
  3. Louis de Branges. Factorization in Kre\i n spaces. J. Funct. Anal., 124(2):228-262, 1994.
  4. Louis de Branges. A conjecture which implies the Riemann hypothesis. J. Funct. Anal., 121(1):117-184, 1994.
  5. Louis de Branges. A construction of invariant subspaces. Math. Nachr., 163:163-175, 1993.
  6. Louis de Branges. The convergence of Euler products. J. Funct. Anal., 107(1):122-210, 1992.
  7. Yi Chu. A note on L. de Branges' paper: “Complementation in Kre\i n spaces” [Trans.Amer.Math.Soc.305 (1988), no.1, 277-291; MR0920159 (89c:46034)]. Northeast. Math. J., 8(1):65-68, 1992.
  8. Louis de Branges. Das mathematische Erbe von Ludwig Bieberbach (1886-1982). Nieuw Arch. Wisk. (4), 9(3):366-370, 1991.
  9. Jacob Korevaar. Laudatio on the Ostrowski Prize for Louis de Branges. Nieuw Arch. Wisk. (4), 9(3):359-365, 1991.
  10. Louis de Branges. A construction of Kre\i n spaces of analytic functions. J. Funct. Anal., 98(1):1-41, 1991.
  11. L. de Branges, I. Gohberg, and J. Rovnyak, editors. Topics in operator theory: Ernst D. Hellinger memorial volume, volume 48 of Operator Theory: Advances and Applications. Birkhäuser Verlag, Basel, 1990.
  12. de Branges receives Ostrowski Prize. Notices Amer. Math. Soc., 37(6):678-679, 1990.
  13. Louis de Branges. Underlying concepts in the proof of the Bieberbach conjecture. ICM Series. American Mathematical Society, Providence, RI, 1988. A plenary address presented at the International Congress of Mathematicians held in Berkeley, California, August 1986, Introduced by Max M. Schiffer.
  14. Louis de Branges. Kre\i n spaces of analytic functions. J. Funct. Anal., 81(2):219-259, 1988.
  15. Louis de Branges. Complementation in Kre\i n spaces. Trans. Amer. Math. Soc., 305(1):277-291, 1988.
  16. Louis de Branges. Underlying concepts in the proof of the Bieberbach conjecture. In Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pages 25-42, Providence, RI, 1987. Amer. Math. Soc.
  17. Louis de Branges. Unitary linear systems whose transfer functions are Riemann mapping functions. In Operator theory and systems (Amsterdam, 1985), volume 19 of Oper. Theory Adv. Appl., pages 105-124. Birkhäuser, Basel, 1986.
  18. Louis de Branges. The story of the verification of the Bieberbach conjecture. In The Bieberbach conjecture (West Lafayette, Ind., 1985), volume 21 of Math. Surveys Monogr., pages 199-203. Amer. Math. Soc., Providence, RI, 1986.
  19. Louis de Branges. Powers of Riemann mapping functions. In The Bieberbach conjecture (West Lafayette, Ind., 1985), volume 21 of Math. Surveys Monogr., pages 51-67. Amer. Math. Soc., Providence, RI, 1986.
  20. Louis de Branges. The Riemann hypothesis for Hilbert spaces of entire functions. Bull. Amer. Math. Soc. (N.S.), 15(1):1-17, 1986.
  21. Louis de Branges. Nodal Hilbert spaces of analytic functions. J. Math. Anal. Appl., 108(2):447-465, 1985.
  22. Louis de Branges. A proof of the Bieberbach conjecture. Acta Math., 154(1-2):137-152, 1985.
  23. Louis de Branges. The expansion theorem for Hilbert spaces of analytic functions. In Topics in operator theory systems and networks (Rehovot, 1983), volume 12 of Oper. Theory Adv. Appl., pages 75-107. Birkhäuser, Basel, 1984.
  24. Louis de Branges. Löwner expansions. J. Math. Anal. Appl., 100(1):323-337, 1984.
  25. Louis de Branges. Consequences of the Cantor construction. J. Math. Anal. Appl., 98(1):198-210, 1984.
  26. Louis de Branges. The comparison theorem for Hilbert spaces of entire functions. Integral Equations Operator Theory, 6(5):603-646, 1983.
  27. Louis de Branges. The invariant subspace problem. Integral Equations Operator Theory, 6(4):488-506, 1983.
  28. Louis de Branges. The Carathéodory-Fejér extension theorem. Integral Equations Operator Theory, 5(2):160-183, 1982.
  29. Louis de Branges. Coefficient estimates. J. Math. Anal. Appl., 82(2):420-450, 1981.
  30. Louis de Branges. Grunsky spaces of analytic functions. Bull. Sci. Math. (2), 105(4):401-416, 1981.
  31. Louis de Branges and David Trutt. Orthogonal Newton polynomials. Adv. in Math., 37(3):251-271, 1980.
  32. Louis de Branges. The Cantor construction. J. Math. Anal. Appl., 76(2):623-630, 1980.
  33. Louis de Branges. Vector lattice topology. J. Math. Anal. Appl., 77(2):451-464, 1980.
  34. Louis de Branges. Vectorial topology. J. Math. Anal. Appl., 69(2):443-454, 1979.
  35. Louis de Branges and David Trutt. Quantum Cesàro operators. In Topics in functional analysis (essays dedicated to M. G. Kre\i n on the occasion of his 70th birthday), volume 3 of Adv. in Math. Suppl. Stud., pages 1-24. Academic Press, New York, 1978.
  36. Louis de Branges. The Riemann mapping theorem. J. Math. Anal. Appl., 66(1):60-81, 1978.
  37. Louis de Branges. Perturbation theory. J. Math. Anal. Appl., 57(2):393-415, 1977.
  38. Louis de Branges. Schrödinger-Dirac spaces of entire functions. J. Math. Anal. Appl., 57(3):653-666, 1977.
  39. Louis de Branges. Coefficients of modular forms. J. Math. Anal. Appl., 45:300-323, 1974.
  40. Louis de Branges. Quaternary modular summations. J. Math. Anal. Appl., 48:680-686, 1974.
  41. Louis de Branges. Examples of modular forms. J. Math. Anal. Appl., 46:358-368, 1974.
  42. Louis de Branges. Modular spaces of entire functions. J. Math. Anal. Appl., 44:192-205, 1973.
  43. Louis de Branges. Hankel spaces of entire functions. J. Math. Anal. Appl., 41:352-372, 1973.
  44. Louis de Branges. Laguerre polynomial spaces. J. Math. Anal. Appl., 41:545-564, 1973.
  45. Richard Bolstein and Louis de Branges. Unsymmetric Gauss spaces. J. Math. Anal. Appl., 44:414-433, 1973.
  46. Louis de Branges. Modular expansions. J. Math. Anal. Appl., 40:303-326, 1972.
  47. Louis de Branges. Gauss spaces of entire functions. J. Math. Anal. Appl., 37:1-41, 1972.
  48. Louis de Branges. Tensor product spaces. J. Math. Anal. Appl., 38:109-148, 1972.
  49. Louis de Branges. Espaces hilbertiens de fonctions entières. Masson et Cie. Éditeurs, Paris, 1972. Traduit de l'anglais par R. Parrot.
  50. Louis de Branges. Lamé-Jacobi spaces of entire functions. J. Math. Anal. Appl., 40:387-408, 1972.
  51. Louis de Branges. The Riemann hypothesis for modular forms. J. Math. Anal. Appl., 35:285-311, 1971.
  52. Louis de Branges. A proof of the Ramanujan hypothesis. J. Math. Anal. Appl., 30:335-352, 1970.
  53. Richard Bolstein and Louis de Branges. Jacobi spaces of entire functions. J. Math. Anal. Appl., 29:589-632, 1970.
  54. Louis de Branges. Factorization and invariant subspaces. J. Math. Anal. Appl., 29:163-200, 1970.
  55. Louis de Branges and David Trutt. Charlier spaces of entire functions. Proc. Amer. Math. Soc., 20:134-140, 1969.
  56. Louis de Branges. The expansion theorem for Hilbert spaces of entire functions. In Entire Functions and Related Parts of Analysis (Proc. Sympos. Pure Math., La Jolla, Calif., 1966), pages 79-148. Amer. Math. Soc., Providence, R.I., 1968.
  57. Louis de Branges and Lawrence Shulman. Perturbations of unitary transformations. J. Math. Anal. Appl., 23:294-326, 1968.
  58. Louis de Branges. Hilbert spaces of entire functions. Prentice-Hall Inc., Englewood Cliffs, N.J., 1968.
  59. Louis de Branges and David Trutt. Meixner and Pollaczek spaces of entire functions. J. Math. Anal. Appl., 22:12-24, 1968.
  60. Louis de Branges and James Rovnyak. Canonical models in quantum scattering theory. In Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965), pages 295-392. Wiley, New York, 1966.
  61. Louis de Branges and James Rovnyak. Square summable power series. Holt, Rinehart and Winston, New York, 1966.
  62. Louis de Branges. Some examples of spaces of entire functions. J. Reine Angew. Math., 222:20-54, 1966.
  63. Louis de Branges. Some Hilbert spaces of analytic functions. III. J. Math. Anal. Appl., 12:149-186, 1965.
  64. Louis de Branges. Some Hilbert spaces of analytic functions. II. J. Math. Anal. Appl., 11:44-72, 1965.
  65. Louis de Branges and James Rovnyak. Correction to “The existence of invariant subspaces”. Bull. Amer. Math. Soc., 71:396, 1965.
  66. Louis de Branges. Self-reciprocal functions. J. Math. Anal. Appl., 9:433-457, 1964.
  67. Louis de Branges and James Rovnyak. The existence of invariant subspaces. Bull. Amer. Math. Soc., 70:718-721, 1964.
  68. Louis de Branges. New and old problems for entire functions. Bull. Amer. Math. Soc., 70:214-223, 1964.
  69. Louis de Branges. Some applications of spaces of entire functions. Canad. J. Math., 15:563-583, 1963.
  70. Louis de Branges. Invariant subspaces of nonselfadjoint transformations. Bull. Amer. Math. Soc., 69:587-590, 1963.
  71. Louis de Branges. A comparison theorem for spaces of entire functions. Proc. Amer. Math. Soc., 14:490-496, 1963.
  72. Louis de Branges. Some Hilbert spaces of analytic functions. I. Trans. Amer. Math. Soc., 106:445-468, 1963.
  73. Louis de Branges. Perturbations of self-adjoint transformations. Amer. J. Math., 84:543-560, 1962.
  74. Louis de Branges. Homogeneous and periodic spaces of entire functions. Duke Math. J., 29:203-224, 1962.
  75. Louis de Branges. Symmetry in spaces of entire functions. Duke Math. J., 29:383-392, 1962.
  76. Louis de Branges. Entire functions and integral transforms. Bull. Amer. Math. Soc., 68:103-106, 1962.
  77. Louis de Branges. Some Hilbert spaces of entire functions. IV. Trans. Amer. Math. Soc., 105:43-83, 1962.
  78. Louis de Branges. Some Hilbert spaces of entire functions. Bull. Amer. Math. Soc., 67:129-134, 1961.
  79. Louis de Branges. Some Hilbert spaces of entire functions. III. Trans. Amer. Math. Soc., 100:73-115, 1961.
  80. Louis de Branges. Some Hilbert spaces of entire functions. II. Trans. Amer. Math. Soc., 99:118-152, 1961.
  81. Louis de Branges. Some Hilbert spaces of entire functions. Trans. Amer. Math. Soc., 96:259-295, 1960.
  82. Louis de Branges. The a-local operator problem. Canad. J. Math., 11:583-592, 1959.
  83. Louis de Branges. The Bernstein problem. Proc. Amer. Math. Soc., 10:825-832, 1959.
  84. Louis de Branges. Some Hilbert spaces of entire functions. Proc. Amer. Math. Soc., 10:840-846, 1959.
  85. Louis de Branges. Some mean squares of entire functions. Proc. Amer. Math. Soc., 10:833 839, 1959.
  86. Louis de Branges. The Stone-Weierstrass theorem. Proc. Amer. Math. Soc., 10:822-824, 1959.
  87. Louis de Branges. Local operators on Fourier transforms. Duke Math. J., 25:143-153, 1958.

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