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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Author: Heinrich Begehr and Robert Gilbert
Title: Transformations, transmutations, and kernel functions, Vol. 1
Additional book information: Longman Publishers, Harlow, 1992, 399 pp., US$79.00. ISBN 3-582-02695-4.

References [Enhancements On Off] (What's this?)

  • [1] Karl Wilhelm Bauer and Stephan Ruscheweyh, Differential operators for partial differential equations and function theoretic applications, Lecture Notes in Mathematics, vol. 791, Springer, Berlin, 1980. MR 584622
  • [2] Steven R. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1228442
  • [3] Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439
  • [4] -, Integral operators in the theory of linear PDE, Ergeb. Math. Grenzgeb. (3), vol. 23, Springer, Berlin, 1961.
  • [5] Stefan Bergman and M. Schiffer, Kernel functions and elliptic differential equations in mathematical physics, Academic Press Inc., New York, N. Y., 1953. MR 0054140
  • [6] L. Bers, Theory of pseudoanalytic functions, NYU Lecture Notes, 1953.
  • [7] Lipman Bers, Mathematical aspects of subsonic and transonic gas dynamics, Surveys in Applied Mathematics, Vol. 3, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0096477
  • [8] A. Bitsadze, Boundary value problems, North-Holland, Amsterdam, 1968.
  • [9] R. W. Carroll, Transmutation and operator differential equations, Notas de Matemática [Mathematical Notes], vol. 67, North-Holland Publishing Co., Amsterdam-New York, 1979. MR 541299
  • [10] Robert Wayne Carroll, Transmutation, scattering theory and special functions, North-Holland Mathematics Studies, vol. 69, North-Holland Publishing Co., Amsterdam-New York, 1982. Notas de Matemática [Mathematical Notes], 87. MR 677111
  • [11] Robert Carroll, Transmutation theory and applications, North-Holland Mathematics Studies, vol. 117, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 105. MR 807146
  • [12] -, Mathematical physics, North-Holland, Amsterdam, 1988.
  • [13] Robert W. Carroll, Topics in soliton theory, North-Holland Mathematics Studies, vol. 167, North-Holland Publishing Co., Amsterdam, 1991. MR 1140704
  • [14] Robert Wayne Carroll and Ralph E. Showalter, Singular and degenerate Cauchy problems, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Mathematics in Science and Engineering, Vol. 127. MR 0460842
  • [15] David L. Colton, Partial differential equations in the complex domain, Pitman Publishing, London-San Francisco, Calif.-Melbourne, 1976. Research Notes in Mathematics, Vol. 4. MR 0481427
  • [16] -, Analytic theory of PDE, Pitman, London, 1980.
  • [17] David L. Colton and Rainer Kress, Integral equation methods in scattering theory, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A Wiley-Interscience Publication. MR 700400
  • [18] R. Courant and D. Hilbert, Methods of mathematical physics, Wiley-Interscience, New York, 1962.
  • [19] A. D. Dzhuraev, Metod singulyarnykh integralnykh uravnenii, “Nauka”, Moscow, 1987 (Russian). MR 938094
  • [20] A. Dzhuraev, Degenerate and other problems, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 61, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1992. MR 1224232
  • [21] L. D. Faddeev and L. A. Takhtajan, Hamiltonian methods in the theory of solitons, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987. Translated from the Russian by A. G. Reyman [A. G. Reĭman]. MR 905674
  • [22] Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639
  • [23] Avner Friedman, Variational principles and free-boundary problems, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1982. A Wiley-Interscience Publication. MR 679313
  • [24] F. D. Gakhov, Boundary value problems, Translation edited by I. N. Sneddon, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. MR 0198152
  • [25] P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
  • [26] Robert P. Gilbert, Constructive methods for elliptic equations, Lecture Notes in Mathematics, Vol. 365, Springer-Verlag, Berlin-New York, 1974. MR 0447784
  • [27] -, Functions theoretic methods in PDE, Academic Press, New York, 1969.
  • [28] Robert P. Gilbert and James L. Buchanan, First order elliptic systems, Mathematics in Science and Engineering, vol. 163, Academic Press, Inc., Orlando, FL, 1983. A function theoretic approach. MR 715259
  • [29] W. Haack and W. Wendland, Lectures on Pfaffian and partial differential equations, Permagon Press, Oxford, 1972.
  • [30] Manfred Kracht and Erwin Kreyszig, Methods of complex analysis in partial differential equations with applications, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1988. A Wiley-Interscience Publication. MR 941372
  • [31] V. D. Kupradze, Potential methods in the theory of elasticity, Translated from the Russian by H. Gutfreund. Translation edited by I. Meroz, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. MR 0223128
  • [32] B. M. \cyr{L}evitan, Teoriya operatorov obobshchennogo sdviga, Izdat. “Nauka”, Moscow, 1973 (Russian). MR 0361916
  • [33] -, Inverse Sturm-Liouville problems, VNU Science Press, Utrecth, 1987.
  • [34] J.-L. Lions, Équations différentielles opérationnelles et problèmes aux limites, Die Grundlehren der mathematischen Wissenschaften, Bd. 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961 (French). MR 0153974
  • [35] V. A. Marchenko, Operatory Shturma-Liuvillya i ikh prilozheniya, Izdat. “Naukova Dumka”, Kiev, 1977 (Russian). MR 0481179
  • [36] Erhard Meister, Randwertaufgaben der Funktionentheorie, Leitfäden der Angewandten Mathematik und Mechanik [Guides to Applied Mathematics and Mechanics], vol. 59, B. G. Teubner, Stuttgart, 1983 (German). Mit Anwendungen auf singuläre Integralgleichungen und Schwingungsprobleme der mathematischen Physik. [With applications to singular integral equations and oscillation problems in mathematical physics]. MR 724255
  • [37] Carlo Miranda, Partial differential equations of elliptic type, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 2, Springer-Verlag, New York-Berlin, 1970. Second revised edition. Translated from the Italian by Zane C. Motteler. MR 0284700
  • [38] N. I. Muskhelishvili, Singular integral equations, Wolters-Noordhoff Publishing, Groningen, 1972. Boundary problems of functions theory and their applications to mathematical physics; Revised translation from the Russian, edited by J. R. M. Radok; Reprinted. MR 0355494
  • [39] -, Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen, 1953.
  • [40] I. Privalov, Randeigenschaften analytischen Funktionen, VEB Deutsch. Verlag Wissen., Berlin, 1956.
  • [41] R. Michael Range, Holomorphic functions and integral representations in several complex variables, Graduate Texts in Mathematics, vol. 108, Springer-Verlag, New York, 1986. MR 847923
  • [42] Y. Rodin, The Riemann BVP on Riemann surfaces, Reidel, Dordrecht, 1988.
  • [43] Menahem Schiffer and Donald C. Spencer, Functionals of finite Riemann surfaces, Princeton University Press, Princeton, N. J., 1954. MR 0065652
  • [44] S. Sitnik and V. Katrakhov, Analytical theory of transmutations with applications, Pitman Press, London (to appear).
  • [45] W. Tutschke, Partielle komplexe Differentialgleichungen in einer und in mehreren komplexen Variablen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1977 (German). Mit losen Berichtigungen; Hochschulbücher für Mathematik, Band 82. MR 0481388
  • [46] I. N. Vekua, Generalized analytic functions, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962. MR 0150320
  • [47] -, New methods for solving elliptic equations, North-Holland, Amsterdam, 1967.
  • [48] Guo Chun Wen and Heinrich G. W. Begehr, Boundary value problems for elliptic equations and systems, Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 46, Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1990. MR 1066209
  • [49] W. L. Wendland, Elliptic systems in the plane, Monographs and Studies in Mathematics, vol. 3, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1979. MR 518816

Review Information:

Reviewer: Robert Carroll
Journal: Bull. Amer. Math. Soc. 30 (1994), 111-117