Bibliography for Cauchy's integral formula

unabridged

 

  1. A Cauchy's integral formula for functions with values in a universal Clifford algebra and its applications.  
    Du, Jinyuan; Zhang, Zhongxiang
    Complex Var. Theory Appl.  47  (2002),  no. 10, 915--928, MathSciNet.   
  2. The Cauchy integral formulas on the octonions.
    Li, Xingmin; Peng, Lizhong
    Bull. Belg. Math. Soc. Simon Stevin 9 (2002), no. 1, 47--64, MathSciNet.   
  3. Discrete analogue of Cauchy's integral formula.
    Khan, Mumtaz Ahmad; Najmi, M.
    Bul. Inst. Politeh. Iasi. Sect. I. Mat. Mec. Teor. Fiz. 45(49) (1999), no. 3-4, 39--44 (2001), MathSciNet.   
  4. On an analogue of Cauchy's formula for Hp,  1/2 <= p < 1, and the Cauchy type integral of a singular measure.
    Rybkin, Alexei
    Complex Variables Theory Appl. 43 (2000), no. 2, 139--149, MathSciNet.   
  5. On the Cauchy integral formula in domains of arbitrary connectivity. (Russian)
    Samokhin, M. V.
    Mat. Sb. 191 (2000), no. 8, 113--130; translation in Sb. Math. 191 (2000), no. 7-8, 1215--1231, MathSciNet.   
  6. Determining the resonator wavelength of VCSELs by Cauchy's integral formula
    Conradi O.
    Optical and Quantum Electronics, October 1999, vol. 31, no. 9/10, pp. 1047-1058(12), Ingenta.   
  7. A generalization of the Cauchy-Hua integral formula on the Lie ball.
    Morimoto, Mitsuo
    Tokyo J. Math. 22 (1999), no. 1, 177--192, MathSciNet.   
  8. Cauchy formula, integral of Cauchy type and Hilbert problem for bianalytic functions.
    Zhen, Zhao
    Partial differential and integral equations (Newark, DE, 1997), 211--218, Int. Soc. Anal. Appl. Comput., 2, Kluwer Acad. Publ., Dordrecht, 1999, MathSciNet.   
  9. Erratum: "Cauchy formula and Cauchy-type integral for a class of generalized analytic functions". (Russian)
    Solovc'ev, Yu. I.
    Izv. Vyssh. Uchebn. Zaved. Mat. 1998, no. 6, 99, MathSciNet.   
  10. Cauchy formula and Cauchy-type integral for a class of generalized analytic functions. (Russian)
    Solovc'ev, Yu. I.
    Izv. Vyssh. Uchebn. Zaved. Mat. 1998, , no. 2, 64--68; translation in Russian Math. (Iz. VUZ) 42 (1998), no. 2, 61--65, MathSciNet.   
  11. Cauchy's Integral Theorem on a Finitely Generated, Real, Commutative, and Associative Algebra
    Pedersen P.S.
    Advances in Mathematics, November 1997, vol. 131, no. 2, pp. 344-356(13), Ingenta.   
  12. Analytic Functions, Cauchy Formula, and Stationary Phase on a Real Abstract Wiener Space
    Malliavin P.; Taniguchi S.
    Journal of Functional Analysis, February 1997, vol. 143, no. 2, pp. 470-528(59), Ingenta.   
  13. Another type of Cauchy's integral formula in complex Clifford analysis.
    Sano, Kimirô
    Tokyo J. Math. 20 (1997), no. 1, 187--204, MathSciNet.   
  14. The Cauchy Integral, Analytic Capacity, and Uniform Rectifiability  
    Pertti Mattila; Mark S. Melnikov; Joan Verdera  
    The Annals of Mathematics, 2nd Ser., Vol. 144, No. 1. (Jul., 1996), pp. 127-136, Jstor.  
  15. Integral formulas of Cauchy type for generalized A-analytic functions. (Russian)
    Kazantsev, S. G.
    Group and metric properties of mappings (Russian), 126--141, Novosibirsk. Gos. Univ., Novosibirsk, 1995, MathSciNet.   
  16. Holomorphy tests based on Cauchy's integral formula.
    Cascante, Carmen; Pascuas, Daniel
    Pacific J. Math. 171 (1995), no. 1, 89--116, MathSciNet.   
  17. A Further Simplification of Dixon's Proof of Cauchy's Integral Theorem (in Notes)  
    Peter A. Loeb  
    American Mathematical Monthly, Vol. 100, No. 7. (Aug. - Sep., 1993), pp. 680-681, Jstor.  
  18. Cauchy integral formula induced by right invertible operators.
    Binderman, Zbigniew
    Demonstratio Math. 25 (1992), no. 3, 671--690, MathSciNet.   
  19. A Note on Dixon's Proof of Cauchy's Integral Theorem (in Notes)  
    Peter A. Loeb  
    American Mathematical Monthly, Vol. 98, No. 3. (Mar., 1991), pp. 242-244, Jstor.   
  20. Cauchy's integral formula in complex Clifford analysis.
    Sano, Kimirô
    Simon Stevin 65 (1991), no. 3-4, 293--317, MathSciNet.   
  21. The Cauchy Integral Formula (in Classroom Computer Capsule)  
    David P. Kraines; Vivian Y. Kraines; David A. Smith  
    The College Mathematics Journal, Vol. 21, No. 4. (Sep., 1990), pp. 327-329, Jstor.   
  22. Cells of harmonicity and generalized Cauchy integral formulae.
    Ryan, John
    Proc. London Math. Soc. (3) 60 (1990), no. 2, 295--318, MathSciNet.   
  23. Cauchy Integral Equalities and Applications  
    Boo Rim Choe  
    Transactions of the American Mathematical Society, Vol. 315, No. 1. (Sep., 1989), pp. 337-352, Jstor.   
  24. The Numerical Evaluation of Cauchy Integrals  
    Bera, Rajendra K.  
    Int. J. of Math. Ed. in Sci. and Tech., (1989), V. 20, No. 5, pp. 763-776.
  25. Convergence of Gauss type product formulas for the evaluation of two-dimensional Cauchy principal value integrals.
    Criscuolo, Giuliana; Mastroianni, Giuseppe
    BIT 27 (1987), no. 1, 72--84, MathSciNet.   
  26. A proof of the differential formula for Cauchy integrals. (Chinese)
    Ye, Shou Zhen
    Qufu Shifan Daxue Xuebao Ziran Kexue Ban 13 (1987), no. 2, 81--82, MathSciNet.   
  27. Index and Cauchy integral formula in complex-quaternionic analysis.
    Bartík, V.; Ferreira, A. V.; Markl, M.; Souvcek, V.
    Simon Stevin 59 (1985), no. 3, 321--329, MathSciNet.   
  28. Shannon's sampling theorem, Cauchy's integral formula, and related results.
    Butzer, Paul L.; Ries, Sigmar; Stens, L.
    Anniversary volume on approximation theory and functional analysis (Oberwolfach, 1983), 363--377, Internat. Schriftenreihe Numer. Math., 65, Birkhäuser, Basel, 1984, MathSciNet.   
  29. The Cauchy integral formula for a class of almost holomorphic functions. (Bulgarian)
    Marinov, M. S.
    Godishnik Vissh. Uchebn. Zaved. Prilozhna Mat. 19 (1983), no. 2, 71--80 (1984), MathSciNet.   
  30. A proof of the formula for the higher derivatives of an integral of Cauchy type. (Chinese)
    Jiang, Run Rong
    Math. Practice Theory 1983, no. 2, 48--50, MathSciNet.   
  31. Cauchy integral formula.
    Souvcek, V.
    Geometry seminars, 1982--1983 (Bologna, 1982/1983), 162--171, Univ. Stud. Bologna, Bologna, 1984, MathSciNet.   
  32. Operators and generalized integral formulas of Cauchy, Schwarz and Poisson. (Russian)
    Bavrin, I. I.
    Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat. 1981, no. 1, 60--62, 87, MathSciNet.   
  33. A Proof of Cauchy's Integral Theorem  
    Flatto, L. and O. Shista
    J. of Approx. Theory, (1973), Vol. 7, pp. 386-390.
  34. Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals.
    Hunter, D. B.
    Numer. Math. 19 (1972), 419--424, MathSciNet.   
  35. A generalization of the integral formulas of Cauchy, Schwarz and Poisson. (Russian)
    Bavrin, I. I.
    Dokl. Akad. Nauk SSSR 202 (1972), 12--15, MathSciNet.   
  36. Shorter Notes: A Brief Proof of Cauchy's Integral Theorem  
    John D. Dixon  
    Proceedings of the American Mathematical Society, Vol. 29, No. 3. (Aug., 1971), pp. 625-626, Jstor.  
  37. Cauchy integral formulas for complex functions.
    Bosh, W.; Krajkiewicz, P.
    Portugal. Math. 30 (1971), 89--92, MathSciNet.   
  38. On the question of generalizing the Cauchy, Schwarz and Poisson integral formulas. (Russian)
    Bavrin, I. I.
    Dokl. Akad. Nauk SSSR 194 1970 250--252, MathSciNet.   
  39. A Proof of the Cauchy Integral Theorem (in Classroom Notes)  
    A. O. Konnully  
    American Mathematical Monthly, Vol. 74, No. 1, Part 1. (Jan., 1967), pp. 54-56, Jstor.  
  40. Gap and inversion formulas for the Cauchy integral.
    Ditzian, Zeev
    J. Math. Anal. Appl. 18 1967 492--503, MathSciNet.   
  41. A certain analogue of the Cauchy integral formula. (Russian)
    Kristalinskiui, R. H.
    Smolensk. Gos. Ped. Inst. Uvcen. Zap. 18 1967 8--21, MathSciNet.   
  42. The Cauchy Integral Theorem (in Classroom Notes)  
    Oswald Wyler  
    American Mathematical Monthly, Vol. 72, No. 1. (Jan., 1965), pp. 50-53, Jstor.  
  43. Sufficient conditions for the validity of Cauchy's integral formula.
    Bagemihl, Frederick
    Proc. Nat. Acad. Sci. U.S.A. 51 1964 380--382, MathSciNet.   
  44. On a certain generalization of the Cauchy integral formula. (French)
    Grinvspun, Z. S.
    1965 Proc. First Kazakh Interuniv. Sci. Conf. on Math. Mech. (October 17-22, 1963) (Russian) pp. 190--192, MathSciNet.   
  45. Remarks on Cauchy's Integral Formula in Matric Spaces  
    Josephine Mitchell  
    Proceedings of the American Mathematical Society, Vol. 11, No. 2. (Apr., 1960), pp. 299-304, Jstor.  
  46. A generalization of Cauchy's integral formula. (Russian)
    Polovziui, G. N.
    Mat. Sbornik N.S. 24(66), (1949). 375--384, MathSciNet.   
  47. Cauchy's integral formula in the theory of analytic functions of several complex variables. (Russian)
    Fuks, B. A.
    Uspehi Matem. Nauk (N. S.) 2, (1947). no. 3(19), 142--157, MathSciNet.   
  48. An extension of Cauchy's integral formula by means of Maxwell's stress tensor.
    Weiss, P.
    J. London Math. Soc. 21, (1946). 210--218, MathSciNet.   
  49. Group Invariance of Cauchy's Formula in Several Variables  
    S. Bochner  
    The Annals of Mathematics, 2nd Ser., Vol. 45, No. 4. (Oct., 1944), pp. 686-707, Jstor.  
  50. Further Generalizations of the Cauchy Integral Formula  
    Dawson G. Fulton  
    American Journal of Mathematics, Vol. 61, No. 4. (Oct., 1939), pp. 843-852, Jstor.  
  51. Generalizations to Higher Dimensions of the Cauchy Integral Formula  
    D. G. Fulton; G. Y. Rainich  
    American Journal of Mathematics, Vol. 54, No. 2. (Apr., 1932), pp. 235-241, Jstor.  
  52. Discussions: A Corollary to Cauchy's Integral Formula (in Questions and Discussions)  
    Norman Miller  
    American Mathematical Monthly, Vol. 35, No. 3. (Mar., 1928), pp. 134-136, Jstor.  
  53. Note on Cauchy's Integral Formula  
    J. L. Walsh  
    The Annals of Mathematics, 2nd Ser., Vol. 18, No. 2. (Dec., 1916), pp. 79-80, Jstor.  

 

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