Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


MathSciNet review: 1568070
Full text of review: PDF   This review is available free of charge.
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?)

  • 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
  • Steven R. Bell, The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1228442
  • 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.
  • 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.
  • 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.
  • 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
  • Robert Wayne Carroll, Transmutation, scattering theory and special functions, Notas de Matemática [Mathematical Notes], vol. 87, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 677111
  • 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.
  • Robert W. Carroll, Topics in soliton theory, North-Holland Mathematics Studies, vol. 167, North-Holland Publishing Co., Amsterdam, 1991. MR 1140704
  • Robert Wayne Carroll and Ralph E. Showalter, Singular and degenerate Cauchy problems, Mathematics in Science and Engineering, Vol. 127, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460842
  • David L. Colton, Partial differential equations in the complex domain, Research Notes in Mathematics, Vol. 4, Pitman Publishing, London-San Francisco, Calif.-Melbourne, 1976. MR 0481427
    • [16]
    -, Analytic theory of PDE, Pitman, London, 1980.
  • 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.
  • A. D. Dzhuraev, Metod singulyarnykh integral′nykh uravneniĭ , “Nauka”, Moscow, 1987 (Russian). MR 938094
  • 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
  • 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, DOI 10.1007/978-3-540-69969-9
  • Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639
  • Avner Friedman, Variational principles and free-boundary problems, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1982. MR 679313
  • F. D. Gakhov, Boundary value problems, Pergamon Press, Oxford-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1966. Translation edited by I. N. Sneddon. MR 0198152
  • P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
  • 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.
  • 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.
  • 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
  • V. D. Kupradze, Potential methods in the theory of elasticity, Israel Program for Scientific Translations, Jerusalem; Daniel Davey & Co., Inc., New York, 1965. Translated from the Russian by H. Gutfreund; Translation edited by I. Meroz. MR 0223128
  • B. M. Levitan, Teoriya operatorov obobshchennogo sdviga, Izdat. “Nauka”, Moscow, 1973 (Russian). MR 0361916
    • [33]
    -, Inverse Sturm-Liouville problems, VNU Science Press, Utrecth, 1987.
  • J.-L. Lions, Équations différentielles opérationnelles et problèmes aux limites, Die Grundlehren der mathematischen Wissenschaften, Band 111, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961 (French). MR 0153974
  • V. A. Marchenko, Operatory Shturma-Liuvillya i ikh prilozheniya, Izdat. “Naukova Dumka”, Kiev, 1977 (Russian). MR 0481179
  • 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, DOI 10.1007/978-3-322-99818-7
  • 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
  • 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.
  • 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, DOI 10.1007/978-1-4757-1918-5
    • [42]
    Y. Rodin, The Riemann BVP on Riemann surfaces, Reidel, Dordrecht, 1988.
  • 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).
  • W. Tutschke, Partielle komplexe Differentialgleichungen in einer und in mehreren komplexen Variablen, Hochschulbücher für Mathematik, Band 82, VEB Deutscher Verlag der Wissenschaften, Berlin, 1977 (German). Mit losen Berichtigungen. MR 0481388
  • I. N. Vekua, Generalized analytic functions, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Company, Inc., Reading, Mass., 1962. MR 0150320
    • [47]
    -, New methods for solving elliptic equations, North-Holland, Amsterdam, 1967.
  • 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, DOI 10.1142/1257
  • 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
    DOI: https://doi.org/10.1090/S0273-0979-1994-00443-4