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Introduction to Complex Analysis pp 19–116Cite as

The Method of Integral Representations in Complex Analysis

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Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 7))

Abstract

Let D be a domain in the complex plane ℂ1 with rectifiable boundary ∂D and f a complex valued function, continuous on \( \overline D \) together with its Cauchy–Riemann derivative:

$$ \frac{{\partial f}} {{\partial \overline z }} = \frac{1} {2}\left( {\frac{{\partial f}} {{\partial x}} + i\frac{{\partial f}} {{\partial y}}} \right),{\text{ }}z = x + iy. $$

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References

  1. Ajrapetyan, R.A.: Boundary properties of an integral of Cauchy-Leray type in piecewise smooth domains in ℂ n, and some applications. Mat. Sb., Nov. Ser. 112, No. 1, 3–23 (1980)

    MathSciNet  Google Scholar 

  2. Ajrapetyan, R.A.: Boundary properties of an integral of Cauchy-Leray type in piecewise smooth domains in ℂ n, and some applications. Math. USSR, Sb. 40, 1–20 (1981). Zbl. 445.32004

    Article  MATH  Google Scholar 

  3. Ajrapetyan, R.A., Khenkin, GM. (=Henkin, G.M,): Analytic continuation of CR-functions through the “edge of the wedge”. Dokl. Akad. Nauk SSSR 259, No. 4, 777–781 (1981)

    MathSciNet  Google Scholar 

  4. Ajrapetyan, R.A., Khenkin, GM. (=Henkin, G.M,): Analytic continuation of CR-functions through the “edge of the wedge”. Sov. Math., Dokl. 24, 129–132 (1981).

    MATH  Google Scholar 

  5. Ajrapetyan, R.A., Khenkin, G.M. (=Henkin, G.M.): Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions I, II. Usp, Mat. Nauk 39, No. 3, 39–106 (1984)

    Google Scholar 

  6. Ajrapetyan, R.A., Khenkin, G.M. (=Henkin, G.M.): Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions I, II. Russ. Math. Surv. 39, No. 3, 41–118 (1984). Zbl. 589.32035

    Article  MATH  Google Scholar 

  7. Ajrapetyan, R.A., Khenkin, G.M. (=Henkin, G.M.): Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions I, II. Mat. Sb., Nov. Ser. 127, No. 1, 92–112 (1985)

    MathSciNet  Google Scholar 

  8. Ajrapetyan, R.A., Khenkin, G.M. (=Henkin, G.M.): Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR-functions I, II. Math. USSR, Sb. 55, No. 1, 91–111 (1986). Zbl. 589.32036

    Article  MATH  Google Scholar 

  9. Ajzenberg, L.A., Yuzhakov, A.P.: Integral representations and residues in multidimensional complex analysis. Nauka, Novosibirsk 1979 [Russian]

    MATH  Google Scholar 

  10. Ajzenberg, L.A., Yuzhakov, A.P.: Integral representations and residues in multidimensional complex analysis. Am. Math. Soc., Providence, R.I. 1983. Zbl. 445.32002

    MATH  Google Scholar 

  11. Amar, E.: Extension de fonctions holomorphes et courants. Bull. Sci. Math., II. Sér. 107, No. 1, 25–48 (1983). Zbl. 543.32007

    MathSciNet  MATH  Google Scholar 

  12. Andreotti, A., Fredricks, G., Nacinovich, M.: On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes. Ann. Sc. Norm. Super. Pisa, CI. Sci., IV. Ser. 8, No. 3, 365–404 (1981). Zbl. 482.35061

    MathSciNet  MATH  Google Scholar 

  13. Baouendi, M.S., Chang, C.H., Treves, F.: Microlocal hypo-analycity and extension of CR-functions. J. Differ. Geom. 18, No. 3, 331–391 (1983). Zbl. 575.32019

    MathSciNet  MATH  Google Scholar 

  14. Baouendi, M.S., Treves, F.: A property of the functions and distributions annihilated by a locally integrable system of complex vector fields. Ann. Math., II. Ser. 113, 387–421 (1981). Zbl. 491.35036

    Article  MathSciNet  MATH  Google Scholar 

  15. Beals, M., Fefferman, Ch., Grossman, R.: Strictly pseudoconvex domains in ℂn. Bull. Am. Math. Soc., New Ser. 8, 125–322 (1983). Zbl. 546.32008

    Article  MathSciNet  MATH  Google Scholar 

  16. Behnke, H., Thullen, P.: Theorie der Funktionen mehrerer komplexer Veränderlichen. Ergebnisse der Mathematik, Springer-Verlag, Berlin 1934. Zbl. 8,365

    MATH  Google Scholar 

  17. Berndtsson, B.: A formula for interpolation and division in ℂn. Math. Ann. 263, No. 4, 399–418 (1983). Zbl. 499.32013

    Article  MathSciNet  MATH  Google Scholar 

  18. Berndtsson, B., Andersson, M.: Henkin-Ramirez kernels with weight factors. Ann. Inst. Fourier 32, No. 3, 91–110 (1982). Zbl. 498.32001

    Article  MathSciNet  MATH  Google Scholar 

  19. Bochner, S., Martin, W.: Several complex variables. Princeton University Press, Princeton 1948. Zbl. 41, 52

    MATH  Google Scholar 

  20. Boggess, A., Pitts, J.: CR extension near a point of higher type. CR. Acad. Sci., Paris, Sér. I 298, No. 1, 9–12 (1984). Zbl. 574.32030

    MathSciNet  MATH  Google Scholar 

  21. Boggess, A., Polking, J.C.: Holomorphic extension of CR-functions. Duke Math. J. 49, No. 4, 757–784 (1982). Zbl. 506.32003

    Article  MathSciNet  MATH  Google Scholar 

  22. Bonneau, P., Cumenge, A., Zeriahi, A.: Division dans les espaces de Lipschitz de fonctions holomorphes. CR. Acad. Sci., Paris, Sér. I 297, No. 9, 517–520 (1983). Zbl. 576.32025

    MathSciNet  MATH  Google Scholar 

  23. Charpentier, Ph.: Résolution de l’équation ∂u =f et application aux zéros des fonctions holomorphes dans le bidisque.: Publ. Math. Orsay 85–02, 126–147 (1985). Zbl. 568.32010

    MathSciNet  Google Scholar 

  24. Chirka, E.M.: Currents and some of their applications. In.: Harvey, R.: Holomorphic chains and their boundaries (Russian translation), Mir, Moscow, 122–154 (1979)

    Google Scholar 

  25. Chirka, E.M., Khenkin, G.M. (= Henkin, G.M.): Boundary properties of holomorphic functions of several complex variables. [In: Current problems in mathematics, vol. 4, 13–142, VINITI, Moscow (1975).] Itogi Nauki Techn., Ser. sovrem. Probl. Mat. 4, 13–142 (1975). Zbl. 335.32001

    Google Scholar 

  26. Dautov, S.A., Khenkin, G.M. (= Henkin, G.M.): Zeros of holomorphic functions of finite order and weighted estimates for solutions of the ∂-equation. Mat. Sb., Nov. Ser. 107, 163–174 (1978)

    MathSciNet  Google Scholar 

  27. Dautov, S.A., Khenkin, G.M. (= Henkin, G.M.): Zeros of holomorphic functions of finite order and weighted estimates for solutions of the ∂-equation. Math. USSR, Sb. 35, 449–459 (1979). Zbl. 392.32001

    Article  MATH  Google Scholar 

  28. Dzhrbashyan, M.M.: Integral transforms and the representation of functions in complex domains. Nauka, Moscow 1966 [Russian]. Zbl. 154,377

    Google Scholar 

  29. Folland, G.B., Kohn, J.J.: The Neumann problem for the Cauchy-Riemann complex. Princeton University Press and University of Tokyo Press, Princeton 1972. Zbl. 247.35093

    MATH  Google Scholar 

  30. Fuks, B.A.: Theory of analytic functions of several complex variables. Nauka, Moscow 1962

    Google Scholar 

  31. Fuks, B.A.: Theory of analytic functions of several complex variables. Am. Math. Soc., Providence, R.I. 1963. Zbl. 138,309

    MATH  Google Scholar 

  32. Fuks, B.A.: Special chapters in the theory of analytic functions of several complex variablesv. Nauka, Moscow 1963

    Google Scholar 

  33. Fuks, B.A.: Special chapters in the theory of analytic functions of several complex variablesv. Transl. Math. Monogr. 14, Am. Math. Soc., Providence, R.I. 1965, Zbl. 146.308

    Google Scholar 

  34. Gamelin, T.W.: Uniform algebras. Prentice-Hall, Englewood Cliffs, N.J. 1969. Zbl. 213,404

    MATH  Google Scholar 

  35. Garnett, J.: Bounded analytic functions. Academic Press, New York 1981. Zbl. 469.30024

    MATH  Google Scholar 

  36. Gindikin, S.G.: Analysis in homogeneous domains. Usp. Mat. Nauk 19, No. 4 (118), 3–92 (1964)

    MathSciNet  MATH  Google Scholar 

  37. Gindikin, S.G.: Analysis in homogeneous domains. Russ. Math. Surv. 19, No. 4, 1–89 (1964). Zbl. 144,81

    Article  MathSciNet  Google Scholar 

  38. Gindikin, S.G., Khenkin, G.M. (=Henkin, G.M.): Integral geometry for ∂-cohomology in q-linear concave domains in ℂℙn. Funkts. Anal. Prilozh. 12, No. 4, 6–23 (1978)

    MathSciNet  MATH  Google Scholar 

  39. Gindikin, S.G., Khenkin, G.M. (=Henkin, G.M.): Integral geometry for ∂-cohomology in q-linear concave domains in ℂℙn. Funct. Anal. Appl. 12, 247–261 (1979). Zbl. 409.32020

    Article  MATH  Google Scholar 

  40. Gindikin, S.G., Khenkin, G.M. (= Henkin, G.M.): The Cauchy-Fantappié formula in projective space. In: Multidimensional complex analysis, 50–63, Krasnoyarsk Inst. Fiziki, 1985 [Russian]: Zbl. 621.32008

    Google Scholar 

  41. Grauert, H.: Kantenkohomologie. Compos. Math. 44, No. 1–3, 79–101 (1981). Zbl. 512.32011

    MathSciNet  MATH  Google Scholar 

  42. Griffiths, Ph., Harris, J.: Principles of algebraic geometry. Wiley, New York 1978. Zbl. 408.14001

    MATH  Google Scholar 

  43. Gruman, L., Lelong, P.: Entire functions of several complex variables. Grundlehren der Mathematischen Wissenschaften 282, Springer-Verlag, Berlin-Heidelberg 1986. Zbl. 583.32001

    Book  MATH  Google Scholar 

  44. Gunning, R.C., Rossi, H.: Analytic functions of several complex variables. Prentice-Hall, Englewood Cliffs, N.J. 1965. Zbl. 141,86

    MATH  Google Scholar 

  45. Hanges, N., Treves, F.: Propagation of holomorphic extendability of CR-functions. Math. Ann. 236, 157–177 (1983). Zbl. 494.32004

    MathSciNet  Google Scholar 

  46. Harvey, R.: Holomorphic chains and their boundaries. Proc. Symp. Pure Math. 30, Part 1, 309–382 (1977). Zbl. 374.32002

    Google Scholar 

  47. Harvey, R., Polking, J.: Fundamental solutions in complex analysis, I, II. Duke Math. J. 46, No. 2, 253–300. Zbl. 441.35043; 301–340 (1979). Zbl. 441.35044

    Article  MathSciNet  MATH  Google Scholar 

  48. Harvey, R., Polking, J.: The ∂-Neumann kernel in the ball in ℂn. Proc. Symp. Pure Math. 41, 117–136 (1984). Zbl. 578.32030

    MathSciNet  Google Scholar 

  49. Henkin, G.M. (= Khenkin, G.M.): Analytic representation for CR-functions on submanifolds of codimension 2 in ℂn. Lect. Notes Math. 798, 169–191 (1980). Zbl. 431.32007

    Article  MathSciNet  Google Scholar 

  50. Henkin, G.M. (= Khenkin, G.M.): Solutions des équations de Cauchy-Riemann tangentielles sur des variétés de Cauchy-Riemann q-concaves. C.R. Acad. Sci., Paris, Sér. A 292, No. 1, 27–30 (1981). Zbl. 472.32014

    MathSciNet  MATH  Google Scholar 

  51. Henkin, G.M. (= Khenkin, G.M.), Leiterer, J.: Theory of functions on complex manifolds. Akademie-Verlag, Berlin 1983. Zbl. 573.32001

    Google Scholar 

  52. Henkin, G.M. (= Khenkin, G.M.), Polyakov, P.L.: Les zéros des fonctions holomorphes d’ordre fini dans le bidisque. C.R. Acad. Sci., Paris. Sér. I 298, No. 2, 5–8 (1984). Zbl. 583.32006

    MATH  Google Scholar 

  53. Henkin, G.M. (= Khenkin, G.M.), Polyakov, P.L.: Prolongement des fonctions holomorphes bornées d’une sous-variété du polydisque. CR. Acad. Sci., Paris, Sér. I 298, No. 4, 221–224 (1984). Zbl. 585.32009

    MATH  Google Scholar 

  54. Hill, CD., Taiani, G.: Families of analytic discs in ℂn with boundaries on a prescribed CR-submanifold. Ann. Sc. Norm. Super. Pisa, CI. Sci., IV. Ser. 5, 327–380 (1978). Zbl. 399.32008

    MathSciNet  MATH  Google Scholar 

  55. Hörmander, L.: L2-estimates and existence theorems for the ∂-operator. Acta Math. 113, No. 1–2, 89–152 (1965). Zbl. 158,110

    Article  MathSciNet  MATH  Google Scholar 

  56. Hörmander, L.: An introduction to complex analysis in several variables. Princeton University Press, Princeton 1966. Zbl. 138,62

    MATH  Google Scholar 

  57. Hua, Loo-keng: Harmonic analysis of functions of several complex variables in the classical domains. Science Press, Peking 1958

    Google Scholar 

  58. Hua, Loo-keng: Harmonic analysis of functions of several complex variables in the classical domains. Am. Math. Soc., Providence, R.I. 1963. Zbl. 112,74

    Google Scholar 

  59. Jöricke, B.: Continuity of the Cauchy projector in Holder norms for classical domains. Math. Nachr. 112, 227–244 (1983). Zbl. 579.32006

    Article  MathSciNet  MATH  Google Scholar 

  60. Kerzman, N, Stein, E.M.: The Szegö kernel in terms of Cauchy-Fantappié kernels. Duke Math. J. 45, No. 2, 197–224 (1978). Zbl. 387.32009

    Article  MathSciNet  MATH  Google Scholar 

  61. Khenkin, G.M. (= Henkin, G.M.): The Lewy equation and analysis on pseudoconvex manifolds I. Usp. Mat. Nauk 32, No. 3, 57–118 (1977)

    MATH  Google Scholar 

  62. Khenkin, G.M. (= Henkin, G.M.): The Lewy equation and analysis on pseudoconvex manifolds I. Russ. Math. Survey 32, No. 3, 59–130 (1977). Zbl. 358.35057

    Article  MATH  Google Scholar 

  63. Khenkin, G.M. (= Henkin, G.M.): The Hartogs-Bochner effect on CR-manifolds. Dokl. Akad. Nauk SSSR 274, 553–558 (1984)

    MathSciNet  Google Scholar 

  64. Khenkin, G.M. (= Henkin, G.M.): The Hartogs-Bochner effect on CR-manifolds. Sov. Math., Dokl. 29, No. 1, 78–82 (1984). Zbl. 601.32021

    MATH  Google Scholar 

  65. Khenkin, G.M. (= Henkin, G.M.): The tangential Cauchy-Riemann equations and the Dirac. Higgs, and Yang-Mills fields. In: Proc. Int. Congr. Math., 809–827, Warszawa 1984. Zbl. 584.58050

    Google Scholar 

  66. Khenkin, G.M. (= Henkin, G.M.), Polyakov, P.L.: Homotopy formulae for the ∂-operator on ℂℙn and the Radon-Penrose transform. Izv. Akad. Nauk SSSR, Ser. Mat. 50, No. 3, 566–597 (1986)

    MathSciNet  MATH  Google Scholar 

  67. Khenkin, G.M. (= Henkin, G.M.), Polyakov, P.L.: Homotopy formulae for the ∂-operator on ℂℙn and the Radon-Penrose transform. Math. USSR, Izv. 28, 555–587 (1987). Zbl. 607.32003

    Article  MATH  Google Scholar 

  68. Khenkin, G.M. (= Henkin, G.M.), Polyakov, P.L.: Residue integral formulas and the Radon-Penrose transform for nonclosed forms. Dokl. Akad. Nauk SSSR 283, 298–303 (1985)

    MathSciNet  Google Scholar 

  69. Khenkin, G.M. (= Henkin, G.M.), Polyakov, P.L.: Residue integral formulas and the Radon-Penrose transform for nonclosed forms. Sov. Math., Dokl. 32, 90–95 (1985). Zbl. 599.32008

    MATH  Google Scholar 

  70. Khenkin, G.M. (= Henkin, G.M.), Sergeev, -A.G.: Uniform estimates for solutions of the ∂-equation in pseudoconvex polyhedra. Mat. Sb., Nov. Ser. 112, No. 4, 522–567 (1980)

    MathSciNet  Google Scholar 

  71. Khenkin, G.M. (= Henkin, G.M.), Sergeev, -A.G.: Uniform estimates for solutions of the ∂-equation in pseudoconvex polyhedra. Math. USSR, Sb. 40, 469–507 (1981). Zbl. 452.32012

    Article  MATH  Google Scholar 

  72. Kohn, J.J.: Methods of P.D.E. in complex analysis. Proc. Symp. Pure Math. 30, No. 1, 215–237 (1977)

    MathSciNet  Google Scholar 

  73. Kohn, J.J.: Subellipticity of the ∂-Neumann problem on pseudoconvex domains: sufficient conditions. Acta Math. 142, No. 1–2, 79–122 (1979). Zbl. 395.35069

    Article  MathSciNet  MATH  Google Scholar 

  74. Koranyi, A., Stein, E.M.: H2-spaces of generalized half-planes. Studia Math. 44, No. 4, 379–388 (1972). Zbl. 236.32003

    MathSciNet  MATH  Google Scholar 

  75. Krantz, S.: Function theory of several complex variables. Wiley, New York 1982. Zbl. 471.32008

    MATH  Google Scholar 

  76. Leray, J.: Le calcul différentiel et intégral sur une variété analytique complexe. Bull. Soc. Math. Fr. 87, 81–180 (1959). Zbl. 199,412

    MathSciNet  MATH  Google Scholar 

  77. Leray, J.: Complément à l’exposé de Waelbroeck: étude spectrale des b-algèbres. Atti delia 2a Riunione del Groupement de Mathématiciens d’expression latine, Firenze-Bologna, 105–110 (1961). Zbl. 145,166

    Google Scholar 

  78. Lieb, I., Range, R.M.: Integral representations on Hermitian manifolds: the ∂-Neumann solution of the Cauchy-Riemann equations. Bull. Am. Math. Soc., New Ser. 11, 355–358 (1984). Zbl. 574.35066

    Article  MathSciNet  MATH  Google Scholar 

  79. Ligocka, E.: The Holder continuity of the Bergman projection and proper holomorphic mappings. Stud. Math. 80, 89–107 (1984). Zbl. 566.32017

    MathSciNet  MATH  Google Scholar 

  80. Lu, Qi-keng: On the Cauchy-Fantappié formula. Acta Math. Sin. 16, No. 3, 344–363 (1966) [Chinese]. Zbl. 173,329

    MATH  Google Scholar 

  81. Manin, Yu. I.: Gauge fields and complex geometry. Nauka, Moscow 1984 [Russian]

    MATH  Google Scholar 

  82. Manin, Yu. I.: Gauge fields and complex geometry. Springer-Verlag, Heidelberg 1988. Zbl. 576.53002

    Google Scholar 

  83. Markushevich, A.I.: Theory of analytic functions. In: Mathematics of the XIX century. Nauka, 115–269, Moscow 1981 [Russian]. Zbl. 506.01013

    Google Scholar 

  84. Nacinovich, M.: Poincaré lemma for tangential Cauchy-Riemann complexes. Math. Ann. 268, No. 4, 449–471 (1984). Zbl. 574.32045

    Article  MathSciNet  MATH  Google Scholar 

  85. Passare, M.: Residues, Currents and their relation to ideals of holomorphic functions. Thesis, Uppsala University 1984

    Google Scholar 

  86. Pellegrino, F.: La théorie des fonctionnelles analytiques et ses applications. In: Levy, P. Problèmes concrets d’analyse fonctionnelle. Gauthier-Villars, 357–470, Paris 1951. Zbl. 43,323

    Google Scholar 

  87. Petrosyan, A.I.: Uniform approximation by polynomials on Weil polyhedra. Izv. Akad. Nauk SSSR, Ser. Mat. 34, 1241–1261 (1970)

    MATH  Google Scholar 

  88. Petrosyan, A.I.: Uniform approximation by polynomials on Weil polyhedra. Math. USSR, Izv. 34, 1250–1271 (1970). Zbl. 217,394

    Article  Google Scholar 

  89. Polyakov, P.L.: Zeros of holomorphic functions of finite order in the polydisc. Mat. Sb., Nov. Ser. 133, No. 1, 103–111 (1987). Zbl. 624.32002

    Google Scholar 

  90. Piatetski-Shapiro, L.I.: Automorphic functions and the geometry of classical domains. Nauka, Moscow 1961

    Google Scholar 

  91. Piatetski-Shapiro, L.I.: Mathematics and its applications, Vol. 8, Gordon and Breach Science Publishers, New York-London-Paris 1969

    Google Scholar 

  92. Piatetski-Shapiro, L.I.: Mathematics and its applications, Vol. 8, Dunod, Paris 1966. Zbl. 137,275

    Google Scholar 

  93. Range, R.M.: Holomorphic functions and integral representations in several complex variables. Springer-Verlag, New York 1986. Zbl. 591.32002

    MATH  Google Scholar 

  94. Ronkin, L.I.: Introduction to the theory of entire functions of several variables. Nauka, Moscow 1971

    MATH  Google Scholar 

  95. Ronkin, L.I.: Introduction to the theory of entire functions of several variables. Amer, Math. Soc., Providence, R.L. 1974. Zbl. 286.32004

    MATH  Google Scholar 

  96. Roos, G.: Fonctions de plusieurs variables complexes et formules de représentation intégrale.: Lecture Notes in Mathematics 1118, 45–182, Springer-Verlag 1986. Zbl, 594.32005

    Google Scholar 

  97. Rossi, H., Vergne, M.: Equations de Cauchy-Riemann tangentielles, associées à un domaine de Siegel. Ann. Sci. Ec. norm, sup, IV. Sér. 9, No. 1, 31–80 (1976). Zbl. 398.32018

    MathSciNet  MATH  Google Scholar 

  98. Rudin, W.: Function theory in the unit ball in ℂn. Springer-Verlag, Berlin 1980. Zbl. 495.32001

    Book  Google Scholar 

  99. Sibony, N.: Un exemple de domaine pseudoconvexe régulier ou l’équation ∂u =f n’admet pas de solution bornée pour/bornée. Invent. Math. 62, No. 2, 235–242 (1980). Zbl. 436.32015

    Article  MathSciNet  Google Scholar 

  100. Stoll, W.: Holomorphic functions of finite order in several complex variables. Reg. Conf. Ser. Math., No. 21, Am. Math. Soc., Providence, R.L. 1974. Zbl. 292.32003

    MATH  Google Scholar 

  101. Treves, F.: Approximation and representation of functions and distributions annihilated by a system of complex vector fields. Ecole Polytechnique, Centre de Mathématiques 1981. Zbl. 515.580030

    MATH  Google Scholar 

  102. Vitushkin, A.G.: Analytic capacity of sets in problems of approximation theory. Usp. Mat. Nauk 22, No. 6, 141–199 (1967)

    MATH  Google Scholar 

  103. Vitushkin, A.G.: Analytic capacity of sets in problems of approximation theory. Russ. Math. Surv. 22, 139–200 (1967). Zbl. 157,394

    Article  MATH  Google Scholar 

  104. Vladimirov, V.S.: Methods of the theory of many complex variables. Nauka, Moscow 1964

    Google Scholar 

  105. Vladimirov, V.S.: Methods of the theory of many complex variables. MIT Press, Cambridge 1966. Zbl. 125, 319

    Google Scholar 

  106. Wells, R.O.: Function theory on differentiable submanifolds. Contributions to analysis. Academic Press, 407–441, New York 1974. Zbl. 293.32001

    Google Scholar 

  107. Wells, R.O.: The Cauchy-Riemann equations and differential geometry. Bull. Am. Math. Soc., New Ser. 6, No. 2, 187–199 (1982). Zbl. 496.32012

    Article  MATH  Google Scholar 

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Khenkin, G.M. (1997). The Method of Integral Representations in Complex Analysis. In: Introduction to Complex Analysis. Encyclopaedia of Mathematical Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61525-2_2

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