Bibliography for The Cauchy-Riemann Equations

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  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. 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.  
  3. 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.   
  4. 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.  
  5. On Symmetric Cauchy--Riemann Manifolds  
    Kaup W.; Zaitsev D.
    Advances in Mathematics, February 2000, vol. 149, no. 2, pp. 145-181(37), Ingenta.   
  6. 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.  
  7. 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.  
  8. The Cauchy Riemann equation on singular spaces.
    Fornæss, John Erik; Gavosto, Estela A.
    Duke Math. J. 93 (1998), no. 3, 453--477, MathSciNet.  
  9. 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.  
  10. 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.  
  11. 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.    
  12. 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.     
  13. 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.  
  14. 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.  
  15. 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.  
  16. On Three-Dimensional Cauchy-Riemann Manifolds  
    Laszlo Lempert  
    Journal of the American Mathematical Society, Vol. 5, No. 4. (Oct., 1992), pp. 923-969, Jstor.  
  17. Hypoellipticity on Cauchy-Riemann Manifolds  
    Johannes A. Petersen  
    Transactions of the American Mathematical Society, Vol. 334, No. 2. (Dec., 1992), pp. 615-639, Jstor.  
  18. 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.  
  19. 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.  
  20. Microlocal analysis of tangential systems of Cauchy-Riemann equations. (Japanese)
    Tajima, Shinichi
    Sugaku 43 (1991), no. 2, 139--150, MathSciNet.  
  21. 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.  
  22. 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.  
  23. 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.  
  24. 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.  
  25. 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.  
  26. 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.  
  27. 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.  
  28. 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.  
  29. 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.  
  30. Generalization of Cauchy--Riemann equations  
    A. K. Kwaniewski
    Reports on Mathematical Physics, Volume 22, Issue 1, August 1985, Pages 133-148, ScienceDirect.     
  31. 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.  
  32. 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.  
  33. 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.  
  34. 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.  
  35. 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.  
  36. Partial difference equations analogous to the Cauchy-Riemann equations.
    Aczél, J.; Haruki, S.
    Funkcial. Ekvac. 24 (1981), no. 1, 95--102, MathSciNet.  
  37. 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.  
  38. 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.  
  39. A Fast Cauchy-Riemann Solver  
    Michael Ghil; Ramesh Balgovind  
    Mathematics of Computation, Vol. 33, No. 146. (Apr., 1979), pp. 585-635, Jstor.  
  40. 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.  
  41. 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.  
  42. 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.  
  43. 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.  
  44. 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.  
  45. Singular integrals and estimates for the Cauchy-Riemann equations.
    Stein, E. M.
    Bull. Amer. Math. Soc. 79 (1973), 440--445, MathSciNet.  
  46. The Tangential Cauchy-Riemann Complex on Spheres  
    G. B. Folland  
    Transactions of the American Mathematical Society, Vol. 171. (Sep., 1972), pp. 83-133, Jstor.  
  47. Similarity principle of the generalized Cauchy-Riemann equations for several complex variables.
    Koohara, Akira
    J. Math. Soc. Japan 23 (1971), 213--249, MathSciNet.  
  48. 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.  
  49. 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.  
  50. Cauchy-Riemann equations in several variables.
    Greenfield, S. J.
    Ann. Scuola Norm. Sup. Pisa (3) 22 1968 275--314, MathSciNet.  
  51. 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.  
  52. A generalization of the Cauchy-Riemann equations.
    Horváth, J.
    Contributions to Differential Equations 1 1963 39--58, MathSciNet.  
  53. 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.  
  54. On Cauchy-Riemann equations in higher dimensions.
    Stiefel, E.
    J. Research Nat. Bur. Standards 48, (1952). 395--398, MathSciNet.  
  55. 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.  
  56. 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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