Book Review
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MathSciNet review:
1568070
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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.
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
- [1]
- K. Bauer and S. Ruscheweyh, Differential operators for PDE and function theoretic applications, Springer, New York, 1980. MR 584622 (82d:35012)
- [2]
- S. Bell, The Cauchy transform, potential theory, and conformal mapping, CRC Press, Boca Raton, FL, 1992. MR 1228442 (94k:30013)
- [3]
- S. Bergman, The kernel function and conformal mapping, Amer. Math. Soc, Providence, RI, 1950. MR 0038439 (12:402a)
- [4]
- -, Integral operators in the theory of linear PDE, Ergeb. Math. Grenzgeb. (3), vol. 23, Springer, Berlin, 1961.
- [5]
- S. Bergman and M. Schiffer, Kernel functions and elliptic PDE in mathematical physics, Academic Press, New York 1953. MR 0054140 (14:876d)
- [6]
- L. Bers, Theory of pseudoanalytic functions, NYU Lecture Notes, 1953.
- [7]
- -, Mathematical aspects of subsonic and transonic gas dynamics, Wiley-Interscience, New York, 1958. MR 0096477 (20:2960)
- [8]
- A. Bitsadze, Boundary value problems, North-Holland, Amsterdam, 1968.
- [9]
- R. Carroll, Transmutation and operator differential equations, North-Holland, Amsterdam, 1979. MR 541299 (80j:35091)
- [10]
- -, Transmutation, scattering theory, and special functions, North-Holland, Amsterdam, 1982. MR 677111 (84b:35114)
- [11]
- -, Transmutation theory and applications, North-Holland, Amsterdam, 1985. MR 807146 (87i:35203)
- [12]
- -, Mathematical physics, North-Holland, Amsterdam, 1988.
- [13]
- -, Topics in soliton theory, North-Holland, Amsterdam, 1991. MR 1140704 (93f:58095)
- [14]
- R. Carroll and R. Showalter, Singular and degenerate Cauchy problems, Academic Press, New York, 1976. MR 0460842 (57:834)
- [15]
- D. Colton, PDE in the complex domain, Pitman, London, 1976. MR 0481427 (58:1543)
- [16]
- -, Analytic theory of PDE, Pitman, London, 1980.
- [17]
- D. Colton and R. Kress, Integral equation methods in scattering theory, Wiley, New York, 1983. MR 700400 (85d:35001)
- [18]
- R. Courant and D. Hilbert, Methods of mathematical physics, Wiley-Interscience, New York, 1962.
- [19]
- A. Dzhuraev, The method of singular integral equations, "Nauka", Moscow, 1987. MR 938094 (89h:35106)
- [20]
- -, Degenerate and other problems, Longman, New York, 1992. MR 1224232 (94j:35058)
- [21]
- L. Faddeev and L. Takhtajan, Hamiltonian methods in the theory of solitons, Springer, New York, 1987. MR 905674 (89m:58103)
- [22]
- G. Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Math., vol. 8, Springer-Verlag, New York, 1965. MR 0209639 (35:536)
- [23]
- A. Friedman, Variational principles and free BVP, Wiley, New York, 1982. MR 679313 (84e:35153)
- [24]
- F. Gakhov, Boundary value problems, Permagon Press, Oxford, 1966. MR 0198152 (33:6311)
- [25]
- P. Garabedian, PDE, Wiley, New York, 1964. MR 0162045 (28:5247)
- [26]
- R. Gilbert, Constructive methods for elliptic equations, Lecture Notes in Math., vol. 365, Springer-Verlag, New York, 1974. MR 0447784 (56:6094)
- [27]
- -, Functions theoretic methods in PDE, Academic Press, New York, 1969.
- [28]
- R. Gilbert and J. Buchanan, First order elliptic systems: A function theoretic approach, Academic Press, New York, 1983. MR 715259 (85d:35035)
- [29]
- W. Haack and W. Wendland, Lectures on Pfaffian and partial differential equations, Permagon Press, Oxford, 1972.
- [30]
- M. Kracht and E. Kreyszig, Methods of complex analysis in PDE with applications, Wiley-Interscience, New York, 1988. MR 941372 (89f:35002)
- [31]
- V. Kupradze, Potential methods in the theory of elasticity, Israel Prog. Scient. Transl., Jerusalem, 1965. MR 0223128 (36:6177)
- [32]
- B. Levitan, Theory of generalized shift operators, 2nd ed, "Nauka", Moscow, 1973. MR 0361916 (50:14358)
- [33]
- -, Inverse Sturm-Liouville problems, VNU Science Press, Utrecth, 1987.
- [34]
- J. L. Lions, Equations différentielles opérationnelles, Springer Berlin, 1961. MR 0153974 (27:3935)
- [35]
- V. Marchenko, Sturm-Liouville operators and their applications, Kiev, 1977. MR 0481179 (58:1317)
- [36]
- E. Meister, Randwertaufgaben der Funktionentheorie, Teubner, Stuttgart, 1983. MR 724255 (85j:30085)
- [37]
- C. Miranda, PDE of elliptic type, Springer, Berlin, 1970. MR 0284700 (44:1924)
- [38]
- N. Muskhelishvili, Singular integral equations, Noordhoff, Groningen, 1953. MR 0355494 (50:7968)
- [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. Range, Holomorphic functions and integral representations in several complex variables, Springer, New York 1986. MR 847923 (87i:32001)
- [42]
- Y. Rodin, The Riemann BVP on Riemann surfaces, Reidel, Dordrecht, 1988.
- [43]
- M. Schiffer and D. Spencer, Functionals of the finite Riemann surface, Princeton Univ. Press, Princeton, NJ, 1954. MR 0065652 (16:461g)
- [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 Deutsch. Verlag Wissen., Berlin, 1977. MR 0481388 (58:1505)
- [46]
- I. Vekua, Generalized analytic functions, Permagon Press, Oxford, 1962. MR 0150320 (27:321)
- [47]
- -, New methods for solving elliptic equations, North-Holland, Amsterdam, 1967.
- [48]
- G. Wen and H. Begehr, Boundary value problems for elliptic equations and systems, Longman, Essex, 1990. MR 1066209 (92a:35002)
- [49]
- W. Wendland, Elliptic systems in the plane, Pitman, London, 1979. MR 518816 (80h:35053)
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