Bibliography for Mobius Transformations

unabridged

 

  1. Transformadas de Möbius e equações de terceiro grau
    José Carlos de Sousa Oliveira Santos
    Boletim da Sociedade Portuguesa de Matemática (nº52, Maio de 2005).  
  2. Linear Fractional Transformation Methods
    Muir Jr. J.R.
    Complex Variables, 1 January 2003, vol. 48, no. 1, pp. 69-81(13), Ingenta.  
  3. Qubit Geometry and Conformal Mapping
    Lee J-w.; Kim C.H.; Lee E.K.; Kim J.; Lee S.
    Quantum Information Processing, April 2002, vol. 1, no. 1-2, pp. 129-134(6), Ingenta.   
  4. Indefinite analogues of j pq-contractive matrix functions and linear fractional transformations.
    Kaltenbäck, Michael
    Acta Sci. Math. (Szeged) 68 (2002), no. 1-2, 349--371, MathSciNet.  
  5. A Note on the Characteristics of Möbius Transformations, II
    Niamsup P.
    Journal of Mathematical Analysis and Applications, September 2001, vol. 261, no. 1, pp. 151-158(8), Ingenta.   
  6. Quaternionic linear fractional transformations and direct isometries of H5.
    Moussafir, Jacques-Olivier
    J. Geom. Phys. 37 (2001), no. 3, 183--189, MathSciNet.  
  7. Analogues of a theorem of Frostman on linear fractional transformations of inner functions and the typical spectral structure of analytic families of weak contractions.
    Ginzburg, Yu. P.
    Operator theory, system theory and related topics (Beer-Sheva/Rehovot, 1997), 323--336, Oper. Theory Adv. Appl., 123, Birkhäuser, Basel, 2001, MathSciNet.  
  8. The Möbius transformation, Green function and the degenerate elliptic equation.
    Ji, Xinhua
    Clifford algebras and their applications in mathematical physics, Vol. 2 (Ixtapa, 1999), 17--35, Progr. Phys., 19, Birkhäuser Boston, Boston, MA, 2000, MathSciNet.  
  9. On Perron's theorem for compositions of linear-fractional transformations. (Russian)  
    Buslaeva, S. F.
    Approximation theory and its applications (Ukranian) (Kiev, 1999),  65--71, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 31, Nats'i onal. Akad. Nauk Ukraïni, Inst. Mat., Kiev, 2000, MathSciNet.  
  10. Linear fractional transformation and disturbance decoupling problem
    Wang J-Z.; Huang L.
    International Journal of Systems Science, 1 June 1999, vol. 30, no. 6, pp. 563-569(7), Ingenta.  
  11. Some properties of a linear-fractional transformation
    Kochina P.Y.; Kochina N.N.
    Journal of Applied Mathematics and Mechanics, 1999, vol. 63, no. 2, pp. 161-163(3), Ingenta.  
  12. Octonionic Möbius transformations.
    Manogue, Corinne A.; Dray, Tevian
    Modern Phys. Lett. A 14 (1999), no. 19, 1243--1255, MathSciNet.  
  13. Holomorphic families of Möbius transformations.
    Noda, Yoji
    Analysis (Munich) 19 (1999), no. 3, 299--307, MathSciNet.  
  14. Free groups of linear-fractional transformations. (Russian)
    Ignatov, Yu. A.; Gruzdeva, T. N.; Sviridova, I. A.
    Izv. Tul. Gos. Univ. Ser. Mat. Mekh. Inform. 5 (1999), no. 1, Matematika, 116--120, MathSciNet.  
  15. Linear fractional transformations and cyclic polynomials.
    Miyake, Katsuya
    Algebraic number theory (Hapcheon/Saga, 1996). Adv. Stud. Contemp. Math. (Pusan) 1 (1999), 137--142, MathSciNet.  
  16. High Speed Sound Sources Localization using Bilinear Time-frequency Transformation
    Poisson F.; Valiere J.C.; Herzog P.
    Applied Acoustics, 3 January 1998, vol. 53, no. 1, pp. 1-13(13), Ingenta.  
  17. Rational approximation of irrational functions by linear fractional transformations.
    Wing, Omar; Jiang, Yao-Lin; Yu, Qing-Jian
    IEEE Trans. Circuits Systems I Fund. Theory Appl. 45 (1998), no. 11, 1216--1221, MathSciNet.  
  18. Möbius transformations and periodic solutions of complex Riccati equations.
    Campos, Juan
    Bull. London Math. Soc. 29 (1997), no. 2, 205--215, MathSciNet.  
  19. Compositions of linear-fractional transformations. (Russian)
    Buslaev, V. I.; Buslaeva, S. F.
    Mat. Zametki 61 (1997), no. 3, 332--338; translation in Math. Notes 61 (1997), no. 3-4, 272--277, MathSciNet.  
  20. A New Characteristic of Mobius Transformations by Use of Apollonius Points of Triangles
    Haruki H.; Rassias T.M.
    Journal of Mathematical Analysis and Applications, January 1996, vol. 197, no. 1, pp. 14-22(9), Ingenta.   
  21. Möbius transformations and monogenic functional calculus.
    Kisil, Vladimir V.
    Electron. Res. Announc. Amer. Math. Soc. 2 (1996), no. 1, 26--33 (electronic), MathSciNet.  
  22. Continued compositions of linear fractional transformations.
    Lorentzen, Lisa
    J. Math. Anal. Appl. 199 (1996), no. 1, 130--137, MathSciNet.  
  23. Convergence of Complex Continued Fractions (in Notes)  
    John Marafino; Timothy J. McDevitt  
    Mathematics Magazine, Vol. 68, No. 3. (Jun., 1995), pp. 202-208, Jstor.  
  24. Some properties of linear-fractional transformations and the harmonic mean of matrix functions.
    Nudel'man, A. A.
    Matrix and operator valued functions, 171--184, Oper. Theory Adv. Appl., 72, Birkhäuser, Basel, 1994, MathSciNet.  
  25. The Symmetry Principle for Mobius Transformations (in Notes)  
    Louis Brickman  
    American Mathematical Monthly, Vol. 100, No. 8. (Oct., 1993), pp. 781-782, Jstor.  
  26. Iteration and bilinear transformations.  
    Short, L.
    Internat. J. Math. Ed. Sci. Tech.  24  (1993),  no. 3, 391--411, MathSciNet.  
  27. Möbius transformations in several dimensions.
    Waterman, P. L.
    Adv. Math. 101 (1993), no. 1, 87--113, MathSciNet.  
  28. The conformal geometry of complex quadrics and the fractional-linear form of Möbius transformations.
    Robinson, Ivor; Trautman, Andrzej
    J. Math. Phys. 34 (1993), no. 11, 5391--5406, MathSciNet.  
  29. Divergent sequences satisfying the linear fractional transformations.
    Mercer, A. McD.
    Internat. J. Math. Math. Sci. 16 (1993), no. 2, 297--299, MathSciNet.  
  30. Outer compositions of hyperbolic/loxodromic linear fractional transformations.
    Gill, John
    Internat. J. Math. Math. Sci. 15 (1992), no. 4, 819--822, MathSciNet.  
  31. Ab initio pair potentials for FCC metals: an application of the method of Mobius transformation
    Mookerjee A.; Chen N.; Kumar V.; Satter M.A.
    Journal of Physics: Condensed Matter, 1992, vol. 4, no. 10, pp. 2439-2448(10), Ingenta.   
  32. Sequences of linear fractional transformations and reverse continued fractions.
    Gill, John
    Continued fractions and orthogonal functions (Loen, 1992), 129--139, Lecture Notes in Pure and Appl. Math., 154, Dekker, New York, 1994, MathSciNet.  
  33. A convergence property for sequences of linear fractional transformations.
    Lorentzen, Lisa
    Continued fractions and orthogonal functions (Loen, 1992), 281--304, Lecture Notes in Pure and Appl. Math., 154, Dekker, New York, 1994, MathSciNet.  
  34. Linear fractional transformations of circular domains in operator spaces.
    Harris, Lawrence A.
    Indiana Univ. Math. J. 41 (1992), no. 1, 125--147, MathSciNet.  
  35. Traces of commutators of Möbius transformations.
    Seppälä, Mika; Sorvali, Tuomas
    Math. Scand. 68 (1991), no. 1, 53--58, MathSciNet.  
  36. Inequalities for Möbius transformations and discrete groups.
    Gehring, F. W.; Martin, G. J.
    J. Reine Angew. Math. 418 (1991), 31--76, MathSciNet.  
  37. On the basic formulas and Vahlen's theorem of the Möbius transformations acting in Rn.
    Fang, Ai Nong
    Hunan Daxue Xuebao 17 (1990), no. 4, 1--9, MathSciNet.  
  38. Conjugacy invariants of Möbius transformations.
    Wada, Masaaki
    Complex Variables Theory Appl. 15 (1990), no. 2, 125--133, MathSciNet.  
  39. Bilinear Basics (in Notes)  
    T. Hoy Booker  
    Mathematics Magazine, Vol. 62, No. 4. (Oct., 1989), pp. 262-267, Jstor.  
  40. Möbius transformations in infinite dimension.
    Frunz\u a, Monica
    Analyse complexe (Bucharest, 1989). Rev. Roumaine Math. Pures Appl. 36 (1991), no. 7-8, 369--376, MathSciNet.  
  41. A distortion theorem for the class of Möbius transformations of convex mappings.
    Ali, Rosihan Mohamed
    Rocky Mountain J. Math. 19 (1989), no. 4, 1083--1094, MathSciNet.  
  42. The class of Möbius transformations of convex mappings.
    Rosihan, Mohamed Ali
    Proceedings of the analysis conference, Singapore 1986, 249--259, North-Holland Math. Stud., 150, North-Holland, Amsterdam, 1988, MathSciNet.  
  43. Linear fractional transformations and companion matrices.
    Pták, Vlastimil
    Comment. Math. Univ. Carolin. 29 (1988), no. 2, 279--284, MathSciNet.  
  44. Curvature, Circles, and Conformal Maps (in Notes)  
    Alan F. Beardon  
    American Mathematical Monthly, Vol. 94, No. 1. (Jan., 1987), pp. 48-53, Jstor.  
  45. Limiting Structures for Sequences of Linear Fractional Transformations  
    Lisa Jacobsen; W. J. Thron  
    Proceedings of the American Mathematical Society, Vol. 99, No. 1. (Jan., 1987), pp. 141-146, Jstor.  
  46. Explicit solutions and linearisation of certain nonlinear evolution equations---bilinear transformation method.
    Ravi, N.; Tamizhmani, K. M.; Lakshmanan, M.
    J. Phys. A 20 (1987), no. 10, 3047--3049, MathSciNet.  
  47. Composition of Linear Fractional Transformations in Terms of Tail Sequences  
    Lisa Jacobsen  
    Proceedings of the American Mathematical Society, Vol. 97, No. 1. (May, 1986), pp. 97-104, Jstor.  
  48. A Property of Inversion in Polar Coordinates  
    Boyd, James N.
    The Math. Teach., (1985), V. 78, No. 1, pp. 60-61.
  49. An Algebraic and Geometric Approach to Two Step Iteration of Bilinear Functions (in The Teaching of Mathematics)  
    Shmuel Avital; Shlomo Libeskind  
    American Mathematical Monthly, Vol. 91, No. 1. (Jan., 1984), pp. 53-56, Jstor.  
  50. A remark on the Möbius transformations. II.
    Gong, Sheng
    Kexue Tongbao (English Ed.) 29 (1984), no. 3, 293--297, MathSciNet.  
  51. Bilinear transformation method.
    Matsuno, Yoshimasa
    Mathematics in Science and Engineering, 174. Academic Press, Inc., Orlando, FL, 1984. viii+223 pp., MathSciNet.  
  52. A general property of the transformation matrices associated with the n-variable bilinear transformation.
    Hertz, David; Zeheb, Ezra
    IEEE Trans. Circuits and Systems 31 (1984), no. 3, 296--299, MathSciNet.  
  53. Linear fractional transformations in rings and modules.
    Young, N. J.
    Linear Algebra Appl. 56 (1984), 251--290, MathSciNet.  
  54. Inversion in a Circle: A Different Kind of Transformation  
    Cohen, Martin P.  
    The Math. Teach., (1983), V. 86, No. 8, pp. 620-623.
  55. Bilinear transformation of multivariable polynomials using the Horner method.
    Smart, Nancy M.; Barnett, Stephen
    Internat. J. Control 37 (1983), no. 4, 861--865, MathSciNet.  
  56. Matrix Möbius transformations.
    Schwarz, Binyamin; Zaks, Abraham
    Comm. Algebra 9 (1981), no. 19, 1913--1968, MathSciNet.  
  57. Fixed points of linear-fractional transformations. (Russian)  
    Sul'man, V. S.
    Funktsional. Anal. i Prilozhen.  14  (1980), no. 2, 93--94, MathSciNet.  
  58. Groups of linear fractional transformations generated by three elements. (Russian)
    Ignatov, Ju. A.
    Mat. Zametki 27 (1980), no. 4, 507--513, 668, MathSciNet.  
  59. Some matrix linear fractional transformations and their properties.
    Karlin, Samuel
    J. Analyse Math. 36 (1979), 145--155 (1980)
  60. Best uniform approximation by linear fractional transformations.
    Bennett, Colin; Rudnick, Karl; Vaaler, Jeffrey D.
    J. Approx. Theory 25 (1979), no. 3, 204--224, MathSciNet.  
  61. Enhancing the convergence region of a sequence of bilinear transformations.
    Gill, John
    Math. Scand. 43 (1978/79), no. 1, 74--80, MathSciNet.  
  62. On discrete groups of Möbius transformations.
    Jørgensen, Troels
    Amer. J. Math. 98 (1976), no. 3, 739--749, MathSciNet.  
  63. Some operators connected with a linear-fractional transformation of the unit circle. (Russian)
    Kir'jackiui, È. G.
    Litovsk. Mat. Sb. 16 (1976), no. 1, 111--122, 247, MathSciNet.  
  64. A family of functions connected with a linear-fractional transformation of the unit circle. (Russian)
    Kir'jackiui, È. G.
    Litovsk. Mat. Sb. 16 (1976), no. 1, 103--110, 247, MathSciNet.  
  65. Mobius Transformations of the Disc and One-Parameter Groups of Isometries of H^p  
    Earl Berkson; Robert Kaufman; Horacio Porta  
    Transactions of the American Mathematical Society, Vol. 199. (Nov., 1974), pp. 223-239, Jstor.  
  66. Certain operators that are connected with a linear-fractional transformation. (Russian)
    Kir'jackiui, È. G.
    Litovsk. Mat. Sb. 14 (1974), no. 1, 57--65, 227--228, MathSciNet.  
  67. Infinite Compositions of Mobius Transformations  
    John Gill  
    Transactions of the American Mathematical Society, Vol. 176. (Feb., 1973), pp. 479-487, Jstor.  
  68. A bilinear transformation.
    Gupta, S. L.
    Math. Education 7 (1973), A41--A42, MathSciNet.  
  69. Continuity of linear fractional transformations on an operator algebra.
    Helton, J. William
    Proc. Amer. Math. Soc. 40 (1973), 217--218, MathSciNet.  
  70. Banach algebras with involution and Möbius transformations.
    Harris, Lawrence A.
    J. Functional Analysis 11 (1972), 1--16, MathSciNet.  
  71. Möbius transformations in stability theory.  
    Smith, Russell A.
    Proc. Cambridge Philos. Soc.  68  1970 143--151, MathSciNet.  
  72. Certain semigroups of linear fractional transformations contain elements of arbitrarily large trace.
    Stolarsky, Kenneth B.
    Illinois J. Math. 14 1970 238--240, MathSciNet.  
  73. Transformation Geometry in the Plane by Complex Number Methods  
    Budden, F. J.  
    The Math. Gazette, (1969) V. 53, No. 383, pp. 19-31.
  74. Groups generated by two parabolic linear fractional transformations.
    Lyndon, R. C.; Ullman, J. L.
    Canad. J. Math. 21 1969 1388--1403, MathSciNet.  
  75. The number of fixed points of a linear-fractional transformation of an operator ball into itself. (Russian)
    Larionov, E. A.
    Mat. Sb. (N.S.) 78 (120) 1969 202--213, MathSciNet.  
  76. On the Iteration of Linear Fractional Transformations  
    Nathan Eljoseph  
    American Mathematical Monthly, Vol. 75, No. 4. (Apr., 1968), pp. 362-366, Jstor.  
  77. Conformal Linear Transformations  
    Ali R. Amir-Moez  
    Mathematics Magazine, Vol. 40, No. 5. (Nov., 1967), pp. 268-270, Jstor.  
  78. Isomorphism of the Möbius and Laguerre transformation groups in noneuclidean planes. (Russian)
    Skopec, Z. A.; Jaglom, I. M.
    Moskov. Gos. Ped. Inst. Ucen. Zap. No. 271 1967 341--361, MathSciNet.  
  79. Groups of elliptic linear fractional transformations.
    Lyndon, R. C.; Ullman, J. L.
    Proc. Amer. Math. Soc. 18 1967 1119--1124, MathSciNet.  
  80. Groups of linear fractional transformations.
    Srebro, U.
    Duke Math. J. 34 1967 49--52, MathSciNet.  
  81. Linear fractional transformations in the plane of t-complex numbers. (Russian)
    Kuzik, G. A.
    Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 189 1966 42--59 (1 foldout), MathSciNet.  
  82. Convergence of sequences of linear fractional transformations and of continued fractions.
    Thron, W. J.
    J. Indian Math. Soc. (N.S.) 27 1963 103--127 (1964), MathSciNet.  
  83. A geometric characterization for a class of discontinuous groups of linear fractional transformations.
    Larcher, H.
    Pacific J. Math. 13 1963 617--627, MathSciNet.  
  84. A necessary and sufficient condition for a discrete group of linear fractional transformations to be discontinuous.
    Larcher, H.
    Duke Math. J. 30 1963 433--436, MathSciNet.  
  85. The Convergence of Sequences with Linear Fractional Recurrence Relation (in Mathematical Notes)  
    Hans Liebeck  
    American Mathematical Monthly, Vol. 68, No. 4. (Apr., 1961), pp. 353-355, Jstor.  
  86. Sequences of linear fractional transformations.
    Erdös, Paul; Piranian, George
    Michigan Math. J 6 1959 205--209, MathSciNet.  
  87. The maximum of the conformal radius of the fundamental region of a group of linear fractional transformations. (Russian)
    Gel'fer, S. A.
    Dokl. Akad. Nauk SSSR 126 1959 463--466, MathSciNet.  
  88. Convergence properties of sequences of linear fractional transformations.
    Piranian, G.; Thron, W. J.
    Michigan Math. J. 4 1957 129--135, MathSciNet.  
  89. Commuting bilinear transformations and matrices.
    Taussky, Olga; Todd, John
    J. Washington Acad. Sci. 46 (1956), 373--375 (1957), MathSciNet.  
  90. A bilinear transformation.
    Watson, G. N.
    Edinburgh Math. Notes 1956 (1956), no. 40, 1--7, MathSciNet.  
  91. The invariant circles of a bilinear transformation.
    Drazin, M. P.
    Math. Gaz. 38, (1954), MathSciNet.  
  92. A note on permutable bilinear transformations.
    Drazin, M. P.
    Math. Gaz. 36, (1952). 30--32, MathSciNet.  
  93. Note on the Arithmetic of Bilinear Transformations  
    Donald M. Adelman  
    Proceedings of the American Mathematical Society, Vol. 1, No. 4. (Aug., 1950), pp. 443-448, Jstor.  
  94. On Series of Iterated Linear Fractional Functions  
    R. D. Carmichael  
    American Journal of Mathematics, Vol. 36, No. 3. (Jul., 1914), pp. 267-288, Jstor.  

 

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(c) John H. Mathews 2003