Bibliography for Harmonic Functions

unabridged

 

  1. On the Representation of a Harmonic Function by a Simple Layer Potential
    Kapanadze D.V.
    Differential Equations, February 2002, vol. 38, no. 2, pp. 259-262(4), Ingenta.   
  2. Certain convex harmonic functions.
    Kim, Yong Chan; Jahangiri, Jay M.; Choi, Jae Ho
    Int. J. Math. Math. Sci. 29 (2002), no. 8, 459--465, MathSciNet.  
  3. High-Precision Mapping of the Magnetic Field Utilizing the Harmonic Function Mean Value Property
    Li L.; Leigh J.S.
    Journal of Magnetic Resonance, February 2001, vol. 148, no. 2, pp. 442-448(7), Ingenta.   
  4. Best approximation in the supremum norm by analytic and harmonic functions.
    Khavinson, Dmitry; Shapiro, Harold S.
    Ark. Mat. 39 (2001), no. 2, 339--359, MathSciNet.  
  5. Meromorphic and harmonic functions inducing continuous maps from M H inf  into the Riemann sphere.
    Suárez, Daniel
    J. Funct. Anal. 183 (2001), no. 1, 164--210, MathSciNet.  
  6. Best approximation in the mean by analytic and harmonic functions.
    Khavinson, Dmitry; McCarthy, John E.; Shapiro, Harold S.
    Indiana Univ. Math. J. 49 (2000), no. 4, 1481--1513, MathSciNet.  
  7. An Entire Holomorphic Function Associated to an Entire Harmonic Function
    Armitage D.H.
    Journal of Approximation Theory, August 1999, vol. 99, no. 2, pp. 325-343(19), Ingenta.   
  8. Boundary Properties of Second-Order Partial Derivatives of the Poisson Integral for a Half-Space
    Topuria S.
    Georgian Mathematical Journal, July 1998, vol. 05, no. 4, pp. 385-400(16), Ingenta.  
  9. Approximation by analytic and harmonic functions, incompressible vector fields, and temperature distributions.
    Lvin, Sergey
    J. Math. Anal. Appl. 225 (1998), no. 2, 652--659, MathSciNet.  
  10. On boundary value problems for conjugate generalized harmonic functions.
    Jaiani, George
    Ricerche Mat. 47 (1998), no. 2, 231--256 (1999), MathSciNet.  
  11. Boundary value problems for analytic and harmonic functions in domains with nonsmooth boundaries. Applications to conformal mappings.
    Khuskivadze, Givi; Kokilashvili, Vakhtang; Paatashvili, Vakhtang
    Mem. Differential Equations Math. Phys. 14 (1998), 195 pp., MathSciNet.  
  12. Three Secrets About Harmonic Functions (in Notes)  
    R. B. Burckel  
    American Mathematical Monthly, Vol. 104, No. 1. (Jan., 1997), pp. 52-56, Jstor.  
  13. Cauchy's problem for harmonic functions with entire data on a sphere.
    Khavinson, Dmitry
    Canad. Math. Bull. 40 (1997), no. 1, 60--66, MathSciNet.  
  14. The Argument Principle for Harmonic Functions (in Notes)  
    Peter Duren; Walter Hengartner; Richard S. Laugesen  
    American Mathematical Monthly, Vol. 103, No. 5. (May, 1996), pp. 411-415, Jstor.  
  15. Extensions of the maximum principle for vector-valued analytic and harmonic functions.
    Dowling, Patrick N.
    J. Math. Anal. Appl. 190 (1995), no. 2, 599--604, MathSciNet.  
  16. Two-dimensional flow in porous strata with conductivity modeling by a harmonic function of the coordinates.
    Pivenc', V. F.
    Fluid Dynam. 30 (1995), no. 3, 418--427, translated from Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza 1995, , no. 3, 102--112(Russian), MathSciNet.  
  17. The Geometry of Harmonic Functions  
    Tristan Needham  
    Mathematics Magazine, Vol. 67, No. 2. (Apr., 1994), pp. 92-108, Jstor.  
  18. Farrell and Mergelyan sets for the space of bounded harmonic functions.
    Pérez-González, Fernando; Trujillo-Gonzalez, Rodrigo
    Classical and modern potential theory and applications (Chateau de Bonas, 1993), 399--412, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 430, Kluwer Acad. Publ., Dordrecht, 1994, MathSciNet.  
  19. Sets of Determination for Harmonic Functions  
    Stephen J. Gardiner  
    Transactions of the American Mathematical Society, Vol. 338, No. 1. (Jul., 1993), pp. 233-243, Jstor.  
  20. Approximation by harmonic functions, and stability of the Dirichlet problem.
    Hedberg, Lars Inge
    Exposition. Math. 11 (1993), no. 3, 193--259. (Reviewer: Joan Verdera) 31-02, MathSciNet.  
  21. Optimal recovery of the derivatives of bounded analytic and harmonic functions from inexact data. (Russian)
    Osipenko, K. Yu.; Stesin, M. I.
    Mat. Zametki 53 (1993), no. 5, 87--97; translation in Math. Notes 53 (1993), no. 5-6, 513--520, MathSciNet.  
  22. Some conjugation problems with second-order derivatives, and their singular cases, for harmonic functions in the plane. (Russian)
    Usmanov, N.
    Dokl. Akad. Nauk Respub. Tadzhikistan 35 (1992), no. 5-6, 237--240 (1993), MathSciNet.   
  23. When Do Orthogonal Families of Curves Possess a Complex Potential?  
    Irl C. Bivens  
    Mathematics Magazine, Vol. 65, No. 4. (Oct., 1992), pp. 226-235, Jstor.  
  24. Geodesics and Bounded Harmonic Functions on Infinite Planar Graphs  
    S. Northshield  
    Proceedings of the American Mathematical Society, Vol. 113, No. 1. (Sep., 1991), pp. 229-233 Jstor.  
  25. Representation of harmonic functions in R4.
    McCoy, Peter A.
    J. Math. Anal. Appl. 154 (1991), no. 1, 43--54, MathSciNet.  
  26. The Dirichlet Problem for a Disk (in Notes)  
    David Minda  
    American Mathematical Monthly, Vol. 97, No. 3. (Mar., 1990), pp. 220-223, Jstor.  
  27. The harmonic conjugate of an algebraic function  
    Edgar, Gerald A. and Lee A. Rubel  
    Am. Math. M., (1990), V. 97 pp. 165-166.  
  28. Uniqueness of Bounded Harmonic Functions  
    Marvin Ortel; Walter Schneider  
    Proceedings of the American Mathematical Society, Vol. 107, No. 4. (Dec., 1989), pp. 937-942, Jstor.  
  29. Approximating continuous functions by holomorphic and harmonic functions.
    Bishop, Christopher J.
    Trans. Amer. Math. Soc. 311 (1989), no. 2, 781--811, MathSciNet.  
  30. p-Harmonic Functions in the Plane  
    Juan J. Manfredi  
    Proceedings of the American Mathematical Society, Vol. 103, No. 2. (Jun., 1988), pp. 473-479, Jstor.  
  31. A Runge Theorem for Harmonic Functions on Closed Subsets of Riemann Surfaces  
    Thomas Bagby  
    Proceedings of the American Mathematical Society, Vol. 103, No. 1. (May, 1988), pp. 160-164, Jstor.  
  32. Short Proofs of Three Theorems on Harmonic Functions  
    H. P. Boas; R. P. Boas  
    Proceedings of the American Mathematical Society, Vol. 102, No. 4. (Apr., 1988), pp. 906-908, Jstor.  
  33. On the Behavior of Harmonic Functions Near a Boundary Point  
    Wade Ramey; David Ullrich  
    Transactions of the American Mathematical Society, Vol. 305, No. 1. (Jan., 1988), pp. 207-220, Jstor.  
  34. Algebras generated by analytic and harmonic functions.
    Axler, Sheldon; Shields, Allen
    Indiana Univ. Math. J. 36 (1987), no. 3, 631--638, MathSciNet.  
  35. Harmonic Functions from a Complex Analysis Viewpoint  
    Sheldon Axler  
    American Mathematical Monthly, Vol. 93, No. 4. (Apr., 1986), pp. 246-258, Jstor.  
  36. On a boundary value problem of harmonic functions.
    Nguyftil en Thù'a Hdo'p
    Acta Math. Vietnam. 11 (1986), no. 1, 105--112, MathSciNet.  
  37. A Heuristic for the Poisson Integral for the Half Plane and some Caveats (in The Teaching of Mathematics)  
    Ridgley Lange; Robert A. Walsh  
    American Mathematical Monthly, Vol. 92, No. 5. (May, 1985), pp. 356-358, Jstor.  
  38. Boundary Behaviour of Level Curves of Harmonic Functions  
    W. J. Walker  
    Proceedings of the American Mathematical Society, Vol. 91, No. 1. (May, 1984), pp. 102-104, Jstor.  
  39. Removable singularities for n-harmonic functions and Hardy classes in polydiscs.
    Singman, David
    Proc. Amer. Math. Soc. 90 (1984), no. 2, 299--302, MathSciNet.   
  40. The Dirichlet Problem: A Mathematical Development  
    Goulet, John  
    Pi Mu Epsilon J., (1983), V. 7, No. 8, pp. 502-511.
  41. Approximation of entire harmonic functions in  R3.
    Kapoor, G. P.; Nautiyal, A.
    Indian J. Pure Appl. Math. 13 (1982), no. 9, 1024--1030, MathSciNet.  
  42. The Dirichlet Problem for Harmonic Functions  
    Ivan Netuka  
    American Mathematical Monthly, Vol. 87, No. 8. (Oct., 1980), pp. 621-628, Jstor.  
  43. Approximation of harmonic functions.
    Dahlberg, Björn E. J.
    Ann. Inst. Fourier (Grenoble) 30 (1980), no. 2, vi, 97--107, MathSciNet.  
  44. The Dirichlet Problem  
    Garding, Lars  
    Math. Intell., (1979), V. 2, No. 1, pp. 43-53.
  45. On Oscillatory Flows  
    Sacksteder, Richard C.  
    Math. Intell., (1978), V. 1, No. 1, pp. 45- 51.  
  46. Relation of the Conjugate Harmonic Functions to f(z) (in Mathematical Notes)  
    E. V. Laitone  
    American Mathematical Monthly, Vol. 84, No. 4. (Apr., 1977), pp. 281-283, Jstor.  
  47. A Note on Harmonic Functions and Harmonic Conjugates  
    Srinivasan, V. K.  
    Int. J. of Math. Ed. in Sci. and Tech., (1977), V. 8, No. 3, pp. 323-328.  
  48. Certain Multiple Valued Harmonic Function  
    L. A. Caffarelli  
    Proceedings of the American Mathematical Society, Vol. 54, No. 1. (Jan., 1976), pp. 90-92, Jstor.  
  49. Harmonic Analysis of Harmonic Functions in the Plane  
    L. A. Rubel  
    Proceedings of the American Mathematical Society, Vol. 54, No. 1. (Jan., 1976), pp. 146-148, Jstor.  
  50. A Converse to the Mean Value Theorem for Harmonic Functions  
    William A. Veech  
    American Journal of Mathematics, Vol. 97, No. 4. (Winter, 1975), pp. 1007-1027, Jstor.  
  51. Inverted Cauchy Problem for the Laplace equation in Engineering Design  
    Nilson, R. H. and Y. G. Tsuei  
    J. of Engineering Math., (1974), Vol 8, No. 4, pp. 329-337.  
  52. Some Half-Plane Dirichlet Problems: A Bare Hands Approach (in Classroom Notes)  
    F. J. Flanigan  
    American Mathematical Monthly, Vol. 80, No. 1. (Jan., 1973), pp. 59-61, Jstor.  
  53. A Representation Formula for Harmonic Functions  
    Chin-Hung Ching; Charles K. Chui  
    Proceedings of the American Mathematical Society, Vol. 39, No. 2. (Jul., 1973), pp.  349-352, Jstor.  
  54. A Solution of Laplace's Equation for a Semi-Infinite Strip  
    Clarence R. Edstrom  
    Mathematics Magazine, Vol. 45, No. 5. (Nov., 1972), pp. 254-259, Jstor.  
  55. Complex Variables: Harmonic and Analytic Functions  
    Flanigan, Francis J.  
    Boston, Allyn and Bacon Pub., Inc., (1972)  
  56. A uniqueness theorem for harmonic functions. Collection of articles dedicated to J. L. Walsh on his 75th birthday, IV (Proc. Internat. Conf. Approximation Theory, Related Topics and their Applications, Univ. Maryland, College Park, Md., 1970).
    Boas, R. P., Jr.
    J. Approximation Theory 5 (1972), 425--427, MathSciNet.   
  57. A Dirichlet Problem  
    Clarence R. Edstrom  
    Mathematics Magazine, Vol. 45, No. 4. (Sep., 1972), pp. 204-205, Jstor.  
  58. On the Mean-Value Property of Harmonic Functions  
    Myron Goldstein; Wellington H. Ow  
    Proceedings of the American Mathematical Society, Vol. 29, No. 2. (Jul., 1971), pp. 341-344, Jstor.  
  59. Complex Methods in Harmonic Analysis  
    Guido Weiss  
    American Mathematical Monthly, Vol. 77, No. 5. (May, 1970), pp. 465-474, Jstor.  
  60. Boundary Functions for Bounded Harmonic Functions  
    T. J. Kaczynski  
    Transactions of the American Mathematical Society, Vol. 137. (Mar., 1969), pp. 203-209, Jstor.  
  61. An Extremal Harmonic Function  
    Kenneth M. Larsen  
    Proceedings of the American Mathematical Society, Vol. 20, No. 2. (Feb., 1969), pp. 333-336, Jstor.  
  62. A generalization of discrete analytic and harmonic functions.
    Hundhausen, Joan Rohrer
    J. Math. Anal. Appl. 25 1969 628--652, MathSciNet.  
  63. On the Boundary Values of Harmonic Functions  
    Richard A. Hunt; Richard L. Wheeden  
    Transactions of the American Mathematical Society, Vol. 132, No. 2. (Jul., 1968), pp. 307-322, Jstor.  
  64. The Level Curves of Harmonic Functions  
    Leopold Flatto; Donald J. Newman; Harold S. Shapiro  
    Transactions of the American Mathematical Society, Vol. 123, No. 2. (Jun., 1966), pp. 425-436, Jstor.  
  65. Minimal harmonic functions on a Riemann surface.
    Sumita, Yukimasa
    Kodai Math. Sem. Rep. 18 1966 51--60, MathSciNet.  
  66. The Poisson Integral for Generalized Half-Planes and Bounded Symmetric Domains  
    Adam Koranyi  
    The Annals of Mathematics, 2nd Ser., Vol. 82, No. 2. (Sep., 1965), pp. 332-350, Jstor.  
  67. On the extension of harmonic functions in three variables.
    Lewy, Hans
    J. Math. Mech. 14 1965 925--927, MathSciNet.   
  68. Classical expansions and their relation to conjugate harmonic functions.
    Muckenhoupt, B.; Stein, E. M.
    Trans. Amer. Math. Soc. 118 1965 17--92, MathSciNet.  
  69. On the Curvature of the Level Lines of a Harmonic Function  
    R. P. Jerrard; L. A. Rubel  
    Proceedings of the American Mathematical Society, Vol. 14, No. 1. (Feb., 1963), pp. 29-32, Jstor.  
  70. On harmonic functions of four variables with rational p4-associates.
    Gilbert, R. P.
    Pacific J. Math. 13 1963 79--96, MathSciNet.  
  71. On the Module of Doubly-Connected Regions Under Harmonic Mappings (in Mathematical Notes)  
    Johannes C. C. Nitsche  
    American Mathematical Monthly, Vol. 69, No. 8. (Oct., 1962), pp. 781-782, Jstor.  
  72. Shorter Notes: On the Mean-Value Property of Harmonic Functions  
    Bernard Epstein  
    Proceedings of the American Mathematical Society, Vol. 13, No. 5. (Oct., 1962), p. 830, Jstor.  
  73. Bodies for Which Harmonic Functions Satisfy the Mean Value Property  
    Avner Friedman; Walter Littman  
    Transactions of the American Mathematical Society, Vol. 102, No. 1. (Jan., 1962), pp. 147-166, Jstor.  
  74. A note on the singularities of harmonic functions in three variables.
    Gilbert, R. P.
    Proc. Amer. Math. Soc. 13 1962 229--232, MathSciNet.  
  75. The boundary values of analytic and harmonic functions.
    Royden, H. L.
    Math. Z. 78 1962 1--24, MathSciNet.  
  76. On degree of approximation by bounded harmonic functions.
    Walsh, J. L.
    J. Math. Pures Appl. (9) 39 1960 201--220, MathSciNet.  
  77. On a Property of Harmonic Functions (in Classroom Notes)  
    H. B. Mann  
    American Mathematical Monthly, Vol. 66, No. 5. (May, 1959), p. 414, Jstor.  
  78. Numerical Analysis and the Dirichlet Problem  
    Donald Greenspan  
    Mathematics Magazine, Vol. 32, No. 4. (Mar. - Apr., 1959), pp. 177-188, Jstor.  
  79. On the Numerical Solution of Dirichlet-Type Problems  
    Donald Greenspan  
    American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), pp. 40-46, Jstor.  
  80. On Pairs of Harmonic Functions  
    R. M. Redheffer  
    Proceedings of the American Mathematical Society, Vol. 8, No. 3. (Jun., 1957), pp. 450-457, Jstor.  
  81. Multivalued harmonic functions in three variables.
    Bergman, Stefan
    Comm. Pure Appl.  Math. 9 (1956), 327--338, MathSciNet.  
  82. Three Dimensional Harmonic Functions Generated by Analytic Functions of a Hypervariable (in Mathematical Notes)  
    E. P. Miles  
    American Mathematical Monthly, Vol. 61, No. 10. (Dec., 1954), pp. 694-697, Jstor.  
  83. Note on Harmonic Functions  
    Henry Helson  
    Proceedings of the American Mathematical Society, Vol. 4, No. 5. (Oct., 1953), pp. 686-691, Jstor.  
  84. Harmonic Functions on Open Riemann Surfaces  
    H. L. Royden  
    Transactions of the American Mathematical Society, Vol. 73, No. 1. (Jul., 1952), pp. 40-94, Jstor.  
  85. A note on harmonic functions and a hydrodynamical application.
    Lewy, Hans
    Proc. Amer. Math. Soc. 3, (1952). 111--113, MathSciNet.  
  86. On harmonic functions and functions of two complex variables with analytic determining functions. (Russian)
    Temlyakov, A. A.
    Uspehi Matem. Nauk (N.S.) 5, (1950). no. 1(35), 240--245, MathSciNet.  
  87. On a method of solving the two-dimensional stress problems solved only by harmonic function.
    Takeuti, Yoitiro
    J. Osaka Inst. Sci. Tech. Part I. 1, (1949). 111--113, MathSciNet.    
  88. Critical points of harmonic functions as positions of equilibrium in a field of force.
    Walsh, J. L.
    Proc. Nat. Acad. Sci. U. S. A. 34, (1948). 111--119, MathSciNet.  
  89. Note on Conjugate Harmonic Functions (in Mathematical Notes)
    Edward Kasner; John De Cicco
    American Mathematical Monthly, Vol. 54, No. 7, Part 1. (Aug. - Sep., 1947), pp. 405-406, Jstor.  
  90. The Harmonic Boundary Value Problem for an Ellipse or an Ellipsoid  
    Dunham Jackson  
    American Mathematical Monthly, Vol. 51, No. 10. (Dec., 1944), pp. 555-563, Jstor.  
  91. Harmonic functions and solutions of the wave equation with three independent variables. (Russian)
    Temliakov, A.
    Rec. Math. [Mat. Sbornik] N.S. 14(56), (1944). 133--154, MathSciNet.  
  92. A study in the uniqueness of harmonic functions.
    Wolf, Frantivsek The Poisson integral.
    Acta Math. 74, (1941). 65--100, MathSciNet.   
  93. On Extending the Definition of a Harmonic Function (in Questions, Discussions, and Notes)  
    J. H. Curtiss  
    American Mathematical Monthly, Vol. 47, No. 4. (Apr., 1940), pp. 225-228, Jstor.  
  94. The Cauchy Problem for Laplace's Equation in Three Dimensions  
    L. H. Johnson, Jr.  
    American Mathematical Monthly, Vol. 42, No. 2. (Feb., 1935), pp. 65-74, Jstor.  
  95. An Intrinsic Treatment of Poisson's Integral  
    Fred W. Perkins  
    American Journal of Mathematics, Vol. 50, No. 3. (Jul., 1928), pp. 389-414, Jstor.  
  96. The Poisson Integral and an Analytic Function on Its Circle of Convergence  
    A. Arwin  
    The Annals of Mathematics, 2nd Ser., Vol. 23, No. 2. (Dec., 1921), pp. 141-143, Jstor.  

 

 

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