Bibliography for The Cauchy-Riemann Equations

unabridged

 

  1. On Maximal Sobolev and Holder Estimates for the Tangential Cauchy-Riemann Operator and Boundary Laplacian  
    Kenneth Douglas Koenig 1973-  
    American Journal of Mathematics, Vol. 124, No. 1. (Feb., 2002), pp. 129-197, Jstor.  
  2. Existence of Generalized Cauchy-Riemann Side-Systems in Several Complex Variables
    Hayashi Y.
    Complex Variables, 1 October 2002, vol. 47, no. 10, pp. 881-889(9), Ingenta.  
  3. Explicit methods for the solution of the generalized Cauchy-Riemann equations and simulation of inviscid rotational flows  
    Roy J.; Hafez M.; Chattot J.  
    J. Computers and Fluids, May 2002, vol. 31, no. 4, pp. 769-786(18), Ingenta.  
  4. Robinson manifolds and Cauchy-Riemann spaces  
    Trautman A.  
    Classical and Quantum Gravity, 2002, vol. 19, no. 2, pp. R1-R10(1), Ingenta.   
  5. The Cauchy--Riemann Equations: Discretization by Finite Elements, Fast Solution of the Second Variable, and a Posteriori Error Estimation  
    Brandts J.
    Advances in Computational Mathematics, November 2001, vol. 15, no. 1-4, pp. 61-77(17), Ingenta.   
  6. On maps of CR manifolds and transformations of differential equations  
    Alexandre Sukhov  
    Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 333, Issue 6, September 2001, Pages 545-550, ScienceDirect.  
  7. Équation de Cauchy--Riemann pour les courants prolongeables -- applications  
    Salomon Sambou  
    Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 332, Issue 6, 15 March 2001, Pages 497-500, ScienceDirect.
  8. Lp-curvature and the Cauchy-Riemann equation near an isolated singular point.
    Harris, Adam; Tonegawa, Yoshihiro
    Nagoya Math. J. 164 (2001), 35--51, MathSciNet.  
  9. Second microlocalization methods for degenerate Cauchy-Riemann equations.
    Lerner, Nicolas
    Carleman estimates and applications to uniqueness and control theory (Cortona, 1999), 109--128, Progr. Nonlinear Differential Equations Appl., 46, Birkhäuser Boston, Boston, MA, 2001, MathSciNet.  
  10. On Symmetric Cauchy--Riemann Manifolds  
    Kaup W.; Zaitsev D.
    Advances in Mathematics, February 2000, vol. 149, no. 2, pp. 145-181(37), Ingenta.   
  11. A Remark on the Reduction of Cauchy-Riemann Manifolds  
    Frank Loose  
    Mathematische Nachrichten, Volume: 214, Issue: 1, Date: June 2000, Pages: 39-51, Wiley InterScience.  
  12. Variétés Cauchy--Riemann homogènes et enveloppes holomorphes  
    Karl Oeljeklaus and Christine Sacré  
    Bulletin des Sciences Mathématiques, Volume 124, Issue 3, April 2000, Pages 193-211, ScienceDirect.     
  13. Convexité et équations de Cauchy-Riemann avec estimations Lp. (French) [Convexity and Cauchy-Riemann equations with Lp-estimates]
    Jouenne, Corinne
    Publ. Mat. 44 (2000), no. 1, 309--323, MathSciNet.  
  14. Simulation of steady compressible flows based on Cauchy/Riemann equations and Crocco's relations. Part II. Viscous flows  
    M. Hafez, W. Guo  
    Int. J. for Numerical Methods in Fluids, Volume: 31, Issue: 1, Date: 15 September 1999, Pages: 325-343, Wiley InterScience.  
  15. Prolongement de courants positifsà travers une sous-variété CR  
    Stéphane Giret  
    Journal des Mathématiques Pures et Appliqués, Volume 78, Issue 9, 9 November 1999, Pages 895-911, ScienceDirect.     
  16. Dolbeault isomorphism in CR manifolds  
    Christine Laurent-Thiébaut and Jürgen Leiterer
    Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 328, Issue 6, 15 March 1999, Pages 469-472, ScienceDirect.  
  17. Optimal weighted estimates for the Cauchy-Riemann equation on analytic polyhedra.
    Cho, Hong Rae; Lee, Jinkee
    Bull. Austral. Math. Soc. 59 (1999), no. 3, 427--431, MathSciNet.  
  18. Simulation of steady compressible flows based on Cauchy/Riemann equations and Crocco's relation
    M. Hafez, W. H. Guo  
    Int. J. for Numerical Methods in Fluids, Volume: 27, Issue: 1-4, Date: January 1998, Pages: 127-138, Wiley InterScience.  
  19. Formules de représentation intégrale et application à la résolution de l'équation de Cauchy-Riemann dans le disque unité généralisé de Mn(C). (French) [Integral representation formulas and application to the solution of the Cauchy-Riemann equation in the generalized unit disk of Mn(C)]
    Hachaichi, Mohamed-Salah
    Maghreb Math. Rev. 7 (1998), no. 2, 101--134, MathSciNet.  
  20. The Cauchy Riemann equation on singular spaces.
    Fornæss, John Erik; Gavosto, Estela A.
    Duke Math. J. 93 (1998), no. 3, 453--477, MathSciNet.  
  21. Analysis of the Cell Vertex Finite Volume Method for the Cauchy-Riemann Equations  
    M. Vanmaele; K. W. Morton; E. Suli; A. Borzi  
    SIAM Journal on Numerical Analysis, Vol. 34, No. 5. (Oct., 1997), pp. 2043-2062, Jstor.  
  22. Cauchy-Riemann equations in a family of convex domains of finite type  
    Corinne Jouenne  
    Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 325, Issue 9, November 1997, Pages 949-952, ScienceDirect.  
  23. On CR-Mappings Between Algebraic Cauchy-Riemann Manifolds and Separate Algebraicity for Holomorphic Functions  
    Ruslan Sharipov; Alexander Sukhov  
    Transactions of the American Mathematical Society, Vol. 348, No. 2. (Feb., 1996), pp. 767-780, Jstor.  
  24. Double-periodic solutions of nonlinear Cauchy-Riemann equations  
    Sergei B. Kuksin  
    Communications on Pure and Applied Mathematics, Volume: 49, Issue: 7, Date: July 1996, Pages: 639-676, Wiley InterScience.  
  25. The Effect of a Nonlinear Viscous Regularization on the Solution of a Cauchy--Riemann Equation  
    Anne C. Morlet  
    Journal of Mathematical Analysis and Applications, Volume 204, Issue 1, 15 November 1996, Pages 236-282, ScienceDirect.     
  26. A successive approximation method for systems of nonlinear Cauchy-Riemann equations. (Chinese)
    Lü, De; Zeng, Yue Sheng
    Huaihua Shizhuan Xuebao 13 (1994), no. 2, 9--12, MathSciNet.  
  27. Partial difference equations analogous to the Cauchy-Riemann equations and related functional equations on rings and fields.
    Haruki, S.; Ng, C. T.
    Results Math. 26 (1994), no. 3-4, 316--323, MathSciNet.  
  28. Uniform estimates for the Cauchy-Riemann equation on q-convex wedges.
    Laurent-Thiébaut, C.; Leiterer, J.
    Ann. Inst. Fourier (Grenoble) 43 (1993), no. 2, 383--436, MathSciNet.  
  29. On Three-Dimensional Cauchy-Riemann Manifolds  
    Laszlo Lempert  
    Journal of the American Mathematical Society, Vol. 5, No. 4. (Oct., 1992), pp. 923-969, Jstor.  
  30. Hypoellipticity on Cauchy-Riemann Manifolds  
    Johannes A. Petersen  
    Transactions of the American Mathematical Society, Vol. 334, No. 2. (Dec., 1992), pp. 615-639, Jstor.  
  31. A fast algorithm to solve nonhomogeneous Cauchy-Riemann equations in the complex plane.
    Daripa, Prabir
    SIAM J. Sci. Statist. Comput. 13 (1992), no. 6, 1418--1432, MathSciNet.  
  32. Elliptic Differential Operators in Harmonic Analysis, I. Generalized Cauchy-Riemann Systems  
    K. M. Davis; J. E. Gilbert; R. A. Kunze  
    American Journal of Mathematics, Vol. 113, No. 1. (Feb., 1991), pp. 75-116, Jstor.  
  33. Microlocal analysis of tangential systems of Cauchy-Riemann equations. (Japanese)
    Tajima, Shinichi
    Sugaku 43 (1991), no. 2, 139--150, MathSciNet.  
  34. Local homotopy formulas for the tangential Cauchy-Riemann equations.
    Trèves, F.
    Partial differential equations and related subjects (Trento, 1990), 238--243, Pitman Res. Notes Math. Ser., 269, Longman Sci. Tech., Harlow, 1992, MathSciNet.  
  35. Solvability of the Cauchy-Riemann equation with constraints on the growth of the functions, and weighted approximation of analytic functions. (Russian)
    Epifanov, O. V.
    Izv. Vyssh. Uchebn. Zaved. Mat. 1990, , no. 2, 49--52; translation in Soviet Math. (Iz. VUZ) 34 (1990), no. 2, 56--59, MathSciNet.  
  36. Yang-Mills fields, the Radon-Penrose transform and the Cauchy-Riemann equations. (Russian) Current problems in mathematics.
    Novikov, R. G.; Khenkin, G. M.
    Fundamental directions, Vol. 54 (Russian), 113--196, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989, MathSciNet.  
  37. A Bochner-Martinelli formula for vector fields which satisfy the generalized Cauchy-Riemann equations.
    Brummelhuis, R. G. M.
    Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 4, 555--566 (1989), MathSciNet.  
  38. Noethericity of generalized Cauchy-Riemann equations. (Russian)
    Mukhamadiev, È.; Baui zaev, S.
    Izv. Akad. Nauk Tadzhik. SSR Otdel. Fiz.-Mat. Khim. i Geol. Nauk 1988, no. 2(108), 3--9, MathSciNet.  
  39. Cauchy-Riemann equations in a class of quaternion functions. (Russian)
    Marinov, M. S.
    Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 23 (1987), no. 2, 107--122 (1988), MathSciNet.  
  40. Corona problems, interpolation problems, and inhomogeneous Cauchy-Riemann equations.
    Garnett, John B.
    Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 917--923, Amer. Math. Soc., Providence, RI, 1987, MathSciNet.  
  41. A Comparative Study of Finite Element and Finite Difference Methods for Cauchy-Riemann Type Equations  
    George J. Fix; Milton E. Rose  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 2. (Apr., 1985), pp. 250-261, Jstor.  
  42. A Kernel Approach to the Local Solvability of the Tangential Cauchy Riemann Equations  
    A. Boggess; M.-C. Shaw  
    Transactions of the American Mathematical Society, Vol. 289, No. 2. (Jun., 1985), pp. 643-658, Jstor.  
  43. Generalization of Cauchy--Riemann equations  
    A. K. Kwaniewski
    Reports on Mathematical Physics, Volume 22, Issue 1, August 1985, Pages 133-148, ScienceDirect.     
  44. A multigrid method for the Cauchy-Riemann equations based on flux-difference splitting and its extension to the steady Euler equations  
    E. Dick  
    Journal of Computational and Applied Mathematics, Volumes 12-13, May 1985, Pages 247-263, ScienceDirect.     
  45. The partial-Neumann Solution to the Inhomogeneous Cauchy-Riemann Equation in the Ball in C^n  
    F. Reese Harvey; John C. Polking  
    Transactions of the American Mathematical Society, Vol. 281, No. 2. (Feb., 1984), pp. 587-613, Jstor.  
  46. On generalized Cauchy-Riemann equations on manifolds. Proceedings of the 12th winter school on abstract analysis (Srní, 1984).
    Burevs, Jarolím; Souvcek, Vladimír
    Rend. Circ. Mat. Palermo (2) 1984, Suppl. No. 6, 31--42, MathSciNet.  
  47. Integral representations on Hermitian manifolds: the partial-Neumann solution of the Cauchy-Riemann equations.
    Lieb, Ingo; Range, R. Michael
    Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 355--358, MathSciNet.  
  48. Tangent Cauchy-Riemann equations and the Yang-Mills, Higgs and Dirac fields.
    Henkin, G. M.
    Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), 809--827, PWN, Warsaw, 1984, MathSciNet.  
  49. Complex differential systems and tangential Cauchy-Riemann equations. (Russian)
    Abrosimov, A. V.
    Mat. Sb. (N.S.) 122(164) (1983), no. 4, 419--434, MathSciNet.  
  50. An Elementary Integral Solution Operator for the Cauchy-Riemann Equations on Pseudoconvex Domains in C^n  
    R. Michael Range  
    Transactions of the American Mathematical Society, Vol. 274, No. 2. (Dec., 1982), pp. 809-816, Jstor.  
  51. Levi Geometry and the Tangential Cauchy-Riemann Equations on a Real Analytic Submanifold of C^n  
    Al Boggess  
    Transactions of the American Mathematical Society, Vol. 272, No. 1. (Jul., 1982), pp. 351-374, Jstor.  
  52. Formules explicites pour les solutions de l'équation de Cauchy-Riemann dans certain domaines. (French) [Explicit formulas for solutions of the Cauchy-Riemann equation in certain domains]
    Hachaichi, M. S.
    C. R. Acad. Bulgare Sci. 35 (1982), no. 10, 1337--1340, MathSciNet.  
  53. A 'Unified' Numerical Treatment of the Wave Equation and the Cauchy-Riemann Equations  
    Milton E. Rose  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 2. (Apr., 1981), pp. 372-376, Jstor.  
  54. Partial difference equations analogous to the Cauchy-Riemann equations.
    Aczél, J.; Haruki, S.
    Funkcial. Ekvac. 24 (1981), no. 1, 95--102, MathSciNet.  
  55. Kernels for the Tangential Cauchy-Riemann Equations  
    Al Boggess  
    Transactions of the American Mathematical Society, Vol. 262, No. 1. (Nov., 1980), pp. 1-49, Jstor.  
  56. Vector cross products, harmonic maps and the Cauchy-Riemann equations.
    Gray, Alfred
    Harmonic maps (New Orleans, La., 1980), pp. 57--74, Lecture Notes in Math., 949, Springer, Berlin-New York, 1982, MathSciNet.  
  57. A Fast Cauchy-Riemann Solver  
    Michael Ghil; Ramesh Balgovind  
    Mathematics of Computation, Vol. 33, No. 146. (Apr., 1979), pp. 585-635, Jstor.  
  58. Higher Order Analogues to the Tangential Cauchy Riemann Equations for Real Submanifolds of C^n with C.R. Singularity  
    Gary Alvin Harris  
    Proceedings of the American Mathematical Society, Vol. 74, No. 1. (Apr., 1979), pp. 79-86, Jstor.  
  59. On the singularity set of complex functions satisfying the Cauchy-Riemann equations.
    Pelling, M. J.
    Michigan Math. J. 26 (1979), no. 2, 225--229, MathSciNet.  
  60. Cauchy-Riemann Differential Equations in Classical Hydrodynamics  
    Roy, S.  
    Int. J. of Math. Ed. in Sci. and Tech., (1979), V. 10, No. 2, p. 291.  
  61. Global behavior of some tangential Cauchy-Riemann equations.
    Burns, Daniel M., Jr.
    Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977), pp. 51--56, Lecture Notes in Pure and Appl. Math., 48, Dekker, New York, 1979, MathSciNet.  
  62. When is a Function that Satisfies the Cauchy-Riemann Equations Analytic?  
    J. D. Gray; S. A. Morris  
    American Mathematical Monthly, Vol. 85, No. 4. (Apr., 1978), pp. 246-256, Jstor.  
  63. The complex Frobenius theorem and uniqueness of solutions to the tangential Cauchy-Riemann equations.
    Hunt, L. R.
    J. Differential Equations 27 (1978), no. 2, 214--223, MathSciNet.  
  64. Unique continuation for solutions to the induced Cauchy-Riemann equations.
    Hunt, L. R.; Polking, J. C.; Strauss, M. J.
    J. Differential Equations 23 (1977), no. 3, 436--447, MathSciNet.  
  65. Is a function that satisfies the Cauchy-Riemann equations necessarily analytic?
    Disney, S. A. R.; Gray, J. D.; Morris, S. A.
    Austral. Math. Soc. Gaz. 2 (1975), no. 3, 67--81, MathSciNet.  
  66. A formula and estimates for the solution of the tangential Cauchy-Riemann equation. (Russian)
    Romanov, A. V.
    Dokl. Akad. Nauk SSSR 220 (1975), 532--535, MathSciNet.  
  67. Propagation of singularities for the Cauchy-Riemann equations.
    Kohn, J. J.
    Complex analysis (Centro Internaz. Mat. Estivo, I Ciclo, Bressanone, 1973) pp. 177--280. Edizioni Cremonese, Rome, 1974, MathSciNet.
  68. Singular integrals and estimates for the Cauchy-Riemann equations.
    Stein, E. M.
    Bull. Amer. Math. Soc. 79 (1973), 440--445, MathSciNet.  
  69. The Tangential Cauchy-Riemann Complex on Spheres  
    G. B. Folland  
    Transactions of the American Mathematical Society, Vol. 171. (Sep., 1972), pp. 83-133, Jstor.  
  70. Denson Complex characteristic coordinates and tangential Cauchy-Riemann equations.
    Andreotti, Aldo; Hill, C.
    Ann. Scuola Norm. Sup. Pisa (3) 26 (1972), 299--324, MathSciNet.  
  71. Similarity principle of the generalized Cauchy-Riemann equations for several complex variables.
    Koohara, Akira
    J. Math. Soc. Japan 23 (1971), 213--249, MathSciNet.  
  72. Removable Sets for Pointwise Solutions of the Generalized Cauchy-Riemann Equations  
    Victor L. Shapiro  
    The Annals of Mathematics, 2nd Ser., Vol. 92, No. 1. (Jul., 1970), pp. 82-101, Jstor.  
  73. Tangential Cauchy-Riemann equations and uniform approximation.
    Freeman, Michael
    Pacific J. Math. 33 1970 101--108, MathSciNet.  
  74. Cauchy-Riemann Relations in n Dimensions (in Brief Versions)  
    T. E. Phipps, Jr.  
    American Mathematical Monthly, Vol. 75, No. 8. (Oct., 1968), pp. 881-882, Jstor.  
  75. Cauchy-Riemann equations in several variables.
    Greenfield, S. J.
    Ann. Scuola Norm. Sup. Pisa (3) 22 1968 275--314, MathSciNet.  
  76. Generalization of the Cauchy-Riemann Equations and Representations of the Rotation Group  
    E. M. Stein; G. Weiss  
    American Journal of Mathematics, Vol. 90, No. 1. (Jan., 1968), pp. 163-196, Jstor.  
  77. A generalization of the Cauchy-Riemann equations.
    Horváth, J.
    Contributions to Differential Equations 1 1963 39--58, MathSciNet.  
  78. A generalisation of the Cauchy-Riemann equations and the harmonicity of monogenic hypercomplex functions. (Russian)
    Morev, I. A.
    Izv. Vysvs. Uvcebn. Zaved. Matematika 1958 1958 no. 3 (4), 176--182, MathSciNet.  
  79. From Generalized Cauchy-Riemann Equations to Linear Algebras  
    James A. Ward  
    Proceedings of the American Mathematical Society, Vol. 4, No. 3. (Jun., 1953), pp. 456-461, Jstor.  
  80. On a property of solutions of a generalized system of Cauchy-Riemann equations. (Russian)
    Vekua, I. N.
    Soobvsvc. Akad. Nauk Gruzin. SSR 14 (1953), 449--453, MathSciNet.  
  81. On Cauchy-Riemann equations in higher dimensions.
    Stiefel, E.
    J. Research Nat. Bur. Standards 48, (1952). 395--398, MathSciNet.  
  82. A Generalization of the Cauchy-Riemann Equations  
    K. P. Williams  
    The Annals of Mathematics, 2nd Ser., Vol. 30, No. 1/4. (1928 - 1929), pp. 206-210, Jstor.  
  83. Concerning Green's Theorem and the Cauchy-Riemann Differential Equations  
    M. B. Porter  
    The Annals of Mathematics, 2nd Ser., Vol. 7, No. 1. (Oct., 1905), pp. 1-2, Jstor.  

 

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