Bibliography for Green's Function

unabridged

 

  1. Iterative Green's Function Analysis of an H-plane T-junction in a parallel-plate Waveguide
    Y.H. Cho
    Journal of Electromagnetic Waves and Applications, 2004, vol. 18, no. 9, pp. 1195-1202(8), Ingenta.
  2. On the Green function for a complement of a finite number of real intervals.
    Andrievskii, V. V.
    Constr. Approx. 20 (2004), no. 4, 565--583, MathSciNet.  
  3. Green's Functions for Multiply Connected Domains via Conformal Mapping  PDF  
    Mark Embree, Lloyd N. Trefethen
    SIAM Review, Volume 41, Number 4, (2003), pp. 745-761, Compendex.
  4. Static Green's Functions with Conformal Mapping and MATLAB
    Mosig, Juan R.  
    IEEE Antennas and Propagation Magazine, v 45, n 5, October, 2003, p 123-135, Compendex.
  5. On Green's function for a bimaterial elastic half-plane
    Martin P.A.
    International Journal of Solids and Structures, May 2003, vol. 40, no. 9, pp. 2101-2119(19), Ingenta.
  6. Application of semigroups to biharmonic Green functions.
    Jakobsson, Stefan
    J. Reine Angew. Math. 563 (2003), 53--82, MathSciNet.  
  7. On growth of Green's function of Sturm-Liouville problem with complex density at the parameter.
    Mamedov, Yu. A.; Mastaliyev, V. Yu.
    Applied problems of mathematics and mechanics (Baku, 2002). Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 17 (2002), 122--127, 206--207, MathSciNet.  
  8. Spectral expansion of the Green function in eigenfunctions of a nonselfadjoint Sturm-Liouville operator on the entire line for a two-layer medium. (Russian)
    Saltykov, E. G.
    Differ. Uravn. 38 (2002), no. 5, 687--691, 719; translation in Differ. Equ. 38 (2002), no. 5, 726--730, MathSciNet.  
  9. Green functions and eigenfunction expansions for the square of the Laplace-Beltrami operator on plane domains.
    Englis, M.; Peetre, J.
    Ann. Mat. Pura Appl. (4) 181 (2002), no. 4, 463--500, MathSciNet.  
  10. Green functions for powers of the Laplace-Beltrami operator.
    Englis, Miroslav
    Function spaces, interpolation theory and related topics (Lund, 2000), 285--309, de Gruyter, Berlin, 2002, MathSciNet.  
  11. Green's Function For A Thermomechanical Mixed Boundary Value Problem Of An Infinite Plane With An Elliptic Hole
    Han J.; Hasebe N.
    Journal of Thermal Stresses, 1 September 2001, vol. 24, no. 9, pp. 903-916(14), Ingenta.  
  12. Problems and Techniques  PDF  
    Joe Flaherty, Section Editor
    SIAM Review, Volume 41, Number 4, (1999), pp. 719-719.
  13. Green functions and conformal geometry.
    Habermann, Lutz; Jost, Jürgen
    J. Differential Geom. 53 (1999), no. 3, 405--442, MathSciNet.  
  14. Green's functions for multiply connected domains via conformal mapping
    Embree, Mark; Trefethen, Lloyd N.
    SIAM Review, v 41, n 4, Dec, 1999, p 745-761, Compendex.
  15. Green's function for a heat source in an infinite region with an arbitrary shaped hole
    Yoshikawa, K.; Hasebe, N.
    Journal of Applied Mechanics, Transactions ASME, v 66, n 1, Mar, 1999, p 204-210, Compendex.
  16. Green's function time-domain boundary element method for the elastodynamic half-plane
    Richter, Christoph; Schmid, Guenther
    International Journal for Numerical Methods in Engineering, v 46, n 5, Oct, 1999, p 627-648, Compendex.
  17. Inradius and integral means for Green's functions and conformal mappings.
    Bañuelos, Rodrigo; Carroll, Tom; Housworth, Elizabeth
    Proc. Amer. Math. Soc. 126 (1998), no. 2, 577--585, MathSciNet.  
  18. Explicit formulas for Green's functions on the annulus and on the Möbius strip.
    Bârza, I.; Ghisa, D.
    Acta Appl. Math. 54 (1998), no. 3, 289--302, MathSciNet.  
  19. The Green functions for weighted biharmonic operators of the form Delta w{-1}\Delta in the unit disk. Some questions of mathematical physics and function theory.
    Shimorin, S. M.
    J. Math. Sci. (New York) 92 (1998), no. 6, 4404--4411, MathSciNet.  
  20. Green's functions for powers of the invariant Laplacian.
    Englis, Miroslav; Peetre, Jaak
    Canad. J. Math. 50 (1998), no. 1, 40--73, MathSciNet.  
  21. Symmetrization, the Green function and conformal mappings. (Russian)
    Dubinin, V. N.
    Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 226 (1996), Anal. Teor. Chisel i Teor. Funktsii. 13, 80--92, 237; translation in J. Math. Sci. (New York) 89 (1998), no. 1, 967--975, MathSciNet.  
  22. Closed-form solutions to surface Green's functions  PDF  
    A. Umerski
    Physical Review B 15 February 1997-Ii Volume 55, Number 8, pp. 55-64.  
  23. The three-dimensional elastostatic Green's function for general anisotropic linear elastic solids.
    Ting, T. C. T.; Lee, Ven-Gen
    Quart. J. Mech. Appl. Math. 50 (1997), no. 3, 407--426, MathSciNet.  
  24. Image method for green's function of anisotropic half-plane with inclined boundary
    Y. Z. C.
    International Journal of Engineering Science, November 1996, vol. 34, no. 14, pp. 1563-1571(9), Ingenta.  
  25. Equivalence of Markov's property and Hölder continuity of the Green function for Cantor-type sets.
    Biaas-Ciez, Leokadia
    East J. Approx. 1 (1995), no. 2, 249--253, MathSciNet.  
  26. The Green function and a generalized corona problem in one complex variable.
    Cegrell, Urban
    New Zealand J. Math. 23 (1994), no. 1, 19--23, MathSciNet.  
  27. Exact conformal-field-theory results on the multi-channel Kondo effect: asymptotic three-dimensional space- and time-dependent multi-point and many-particle Green's functions.
    Ludwig, Andreas W. W.; Affleck, Ian
    Nuclear Phys. B 428 (1994), no. 3, 545--611, MathSciNet.  
  28. Exploring the Complex Plane: Green's Functions, Hilbert Transforms, and Analytic Continuation
    P. Singh; William J. Thompson    
    Computers in Physics, Vol. 7, Issue 4, (1993), pp. 388-392.
  29. A-infty and the Green function.
    Wu, Jang-Mei
    Pacific J. Math. 157 (1993), no. 1, 159--178, MathSciNet.  
  30. Analytic continuation with respect to a parameter in a neighborhood of zero of the Green function of basic exterior boundary value problems for the Helmholtz equation. (Russian)
    Suveika, I. V.
    Izv. Akad. Nauk Respub. Moldova Mat. 1993, no. 1, 23--29, 107, 109, MathSciNet.  
  31. Derivation of Green's Function of Complex Structures Using Computer Algebra
    Fabunmi, J. and Chang, P.
    AIAA Journal, Vol. 30, No. 10, (1992), pp. 2540-2570.
  32. On the Green function for a multiconnected domain.
    Rzolhk adkowski, Grzegorz
    Classical analysis (Kazimierz Dolny, 1991), 233--246, World Sci. Publishing, River Edge, NJ, 1992, MathSciNet.  
  33. The Near-Field Singularity Predicted by the Spiral Green's Function in Acoustics and Electrodynamics
    H. Ardavan
    Proceedings: Mathematical and Physical Sciences, Vol. 433, No. 1888 (May, 1991), pp. 451-459, Jstor.    
  34. Green's function for the anisotropic half-plane loaded by a single force
    Becker, W.
    Ingenieur-Archiv, v 60, n 4, 1990, p 255-261, Compendex.
  35. Complex variable Green's function representation of plane inelastic deformation in isotropic solids
    Denda, M.  
    Acta Mechanica, v 72, n 3-4, Jun, 1988, p 205-221, Compendex.
  36. Closed set of equations for Green functions in conformal invariant quantum field theory.
    Fradkin, E. S.; Pal'chik, M. Ya.
    Wandering in the fields, 128--143, World Sci. Publishing, Singapore, 1987, MathSciNet.  
  37. The Green functions in curved spacetime.
    Buchbinder, I. L.; Kirillova, E. N.; Odintsov, S. D.
    Classical Quantum Gravity 4 (1987), no. 3, 711--719, MathSciNet.  
  38. Green's Function Solution For Plane Anisotropic Contact Problems.
    Miller, G. R.  
    Journal of Applied Mechanics, Transactions ASME, v 53, n 2, Jun, 1986, p 386-389, Compendex.
  39. Generalized Green's functions and spectral densities in the complex energy plane.
    Engdahl, Erik; Brändas, Erkki; Rittby, Magnus; Elander, Nils
    J. Math. Phys. 27 (1986), no. 11, 2629--2639, MathSciNet.  
  40. Green's function, Jensen measures, and bounded point evaluations.
    Anderson, Stephen L.
    J. Funct. Anal. 43 (1981), no. 3, 360--367, MathSciNet.  
  41. On Green functions of fundamental boundary value problems for the Helmholtz equation in the exterior of a compact domain. (Russian)
    Suveika, I. V.
    Boundary value problems for partial differential equations. Mat. Issled. No. 63 (1981), 142--150, 184, MathSciNet.  
  42. On the torsion function, Green's function and conformal radius: an isoperimetric inequality of Pólya and Szegö, some extensions and applications.
    Hersch, Joseph
    J. Analyse Math. 36 (1979), 102--117 (1980), MathSciNet.  
  43. Green's function for the heat equation as a limit of product integrals.
    Koosis, Paul
    Ark. Mat. 16 (1978), no. 2, 153--159, MathSciNet.  
  44. The Green's Function and Determining Equations
    David A. Sanchez
    The American Mathematical Monthly, Vol. 82, No. 7 (Aug., 1975), pp. 747-749, Jstor.   
  45. Variation Of The Green's Function Due To Quasiconformal Distortion Of The Region.
    Sontag, Alexia
    Archive for Rational Mechanics and Analysis, v 59, n 3, 1975, p 257-280, Compendex.
  46. Representation theory of the universal covering of the Euclidean conformal group and conformal invariant Green's functions.
    Grensing, G.
    J. Mathematical Phys. 16 (1975), 312--317, MathSciNet.  
  47. Variation of the Green's function due to quasiconformal distortion of the region.
    Sontag, Alexia
    Arch. Rational Mech. Anal. 59 (1975), no. 3, 257--280, MathSciNet.  
  48. The discrete Green's function and the discrete kernel function.
    Deeter, Charles R.; Gray, J. Michael
    Discrete Math. 10 (1974), 29--42, MathSciNet.  
  49. Conformal expansion for Euclidean Green functions.
    Todorov, I. T.
    Group theoretical methods in physics (Proc. Third Internat. Colloq., Centre Phys. Théor., Marseille, 1974), Vol. 1, pp. 160--170. Centre Nat. Recherche Sci., Centre Phys. Théor., Marseille, 1974, MathSciNet.  
  50. Analyticity properties and asymptotic expansions of conformal covariant Green's functions.
    Ferrara, S.; Grillo, A. F.; Gatto, R.; Parisi, G.
    Nuovo Cimento A (11) 19 (1974), 667--695, MathSciNet.  
  51. On the Green's function for the biharmonic equation in an infinite wedge.
    Seif, Joseph B.
    Trans. Amer. Math. Soc. 182 (1973), 241--260, MathSciNet.  
  52. Derivation Of Weight Functions For The Circular And Rectangular Channel Magnetic Flowmeters, By Means Of Green's Theorem And Conformal Mapping
    Smyth C. C.
    J Phys E Sci Instrum, v 4, n 1, Jan, 1971, p 29-34, Compendex.
  53. Representing measures for R(X) and their Green's functions.
    Sarason, Donald
    J. Functional Analysis 7 (1971), 359--385, MathSciNet.  
  54. An approximate construction of the Green's function and of a conformal mapping. (Russian)
    Fominyh, Ju. F.
    Perm. Gos. Univ. U\v cen. Zap. No. 218 (1969), 60--62, MathSciNet.  
  55. Behavior near the boundary of the Green's function for a process of Brownian motion with reflexion. (Russian)
    Rozental , A. L.
    Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 1969 no. 6, 43--49, MathSciNet.  
  56. Poles of the Two-Body Green Function
    H. Osborn
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 302, No. 1468 (Dec., 1967), pp. 137-144, Jstor.   
  57. Determination of the critical exponent of the Green's function.
    Loewner, Charles
    1966 Contemporary Problems in Theory Anal. Functions (Internat. Conf., Erevan 1965) (Russian) pp. 184--187, MathSciNet.  
  58. Utilizing Green's Function to Solve Nonhomogeneous Differential Systems
    L. C. Barrett; R. A. Jacobson
    The American Mathematical Monthly, Vol. 70, No. 1 (Jan., 1963), pp. 65-68, Jstor.   
  59. Analytic properties of the time Green functions in the statistical mechanics of many-body systems.
    Revzen, M.; Trainor, L. E. H.
    Phys. Lett. 2 1962 301--303, MathSciNet.  
  60. Lectures on the Green's function method.
    Prange, R. E.
    1962 Lectures on the many-body problem pp. 115--132, MathSciNet.  
  61. The Circles of Curvature of the Curves of Steepest Descent of Green's Function
    J. L. Walsh
    The American Mathematical Monthly, Vol. 68, No. 4 (Apr., 1961), pp. 323-329, Jstor.   
  62. Lagging and anticipating Green functions in the theory of ferromagnetism. (Russian)
    Tyablikov, S. V.
    Ukrain. Mat. \v Z. 11 1959 287--294, MathSciNet.  
  63. Note on the Shape of Level Curves of Green's Function
    J. L. Walsh
    The American Mathematical Monthly, Vol. 60, No. 10 (Dec., 1953), pp. 671-674, Jstor.   
  64. Construction of the Green's Function of a Linear Differential System
    Kenneth S. Miller
    Mathematics Magazine, Vol. 26, No. 1 (Sep., 1952), pp. 1-8, Jstor.   
  65. A Green's Function in the Theory of Functions of Several Complex Variables
    P. R. Garabedian
    The Annals of Mathematics, 2nd Ser., Vol. 55, No. 1 (Jan., 1952), pp. 19-33, Jstor.     
  66. On the Green Function of a Star-Shaped Three Dimensional Region
    S. E. Warschawski
    The American Mathematical Monthly, Vol. 57, No. 7 (Aug., 1950), pp. 471-473, Jstor.   
  67. Variation of the Green Function and Theory of the p-Valued Functions
    Menahem Schiffer
    American Journal of Mathematics, Vol. 65, No. 2 (Apr., 1943), pp. 341-360, Jstor.    
  68. Green's Function and the Problem of Plateau
    Jesse Douglas
    American Journal of Mathematics, Vol. 61, No. 3 (Jul., 1939), pp. 545-589, Jstor.   
  69. On the Shape of Level Curves of Green's Function
    J. L. Walsh
    The American Mathematical Monthly, Vol. 44, No. 4 (Apr., 1937), pp. 202-213, Jstor.   
  70. Note on the Curvature of Level Curves of Green's Function
    J. L. Walsh
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 2 (Feb., 1937), pp. 84-89, Jstor.   
  71. Note on the Curvature of Orthogonal Trajectories of Level Curves of Green's Function
    J. L. Walsh
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 23, No. 3 (Mar., 1937), pp. 166-169, Jstor.    
  72. Lemniscates and Equipotential Curves of Green's Function
    J. L. Walsh
    The American Mathematical Monthly, Vol. 42, No. 1 (Jan., 1935), pp. 1-17, Jstor.   
  73. The Green's Function for a Plane Contour
    Hobart Dickinson Frary
    American Journal of Mathematics, Vol. 42, No. 1 (Jan., 1920), pp. 11-25, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006