Book Review
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MathSciNet review:
1567166
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Book Information:
Author:
Martin Schechter
Title:
Modern methods in partial differential equations, an introduction
Additional book information:
McGraw-Hill, New York, 1977, xv + 245 pp.
Shmuel Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. MR 0178246
S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623–727. MR 125307, DOI 10.1002/cpa.3160120405
P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
R. Courant and D. Hilbert, Shu-hsüeh wu-li fang fa. Chüan I, Science Press, Peking, 1965 (Chinese). Translated from the English by Ch’ien Min and Kuo Tun-jen. MR 0195654
J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269. MR 388464, DOI 10.1007/BF02392165
6. Y. V. Egorov, On canonical transformations of pseudodifferential equations, Uspehi Mat. Nauk 25 (1969), 235-236.
7. L. Ehrenpreis, Fourier analysis in the complex domain, Wiley, New York, 1970.
Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088
Avner Friedman, Stochastic differential equations and applications. Vol. 1, Probability and Mathematical Statistics, Vol. 28, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0494490
G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403
P. R. Garabedian, Partial differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0162045
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443
Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York, Inc., New York, 1969. Third revised printing. MR 0248435
Lars Hörmander, Pseudo-differential operators and hypoelliptic equations, Singular Integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966) Amer. Math. Soc., Providence, R.I., 1967, pp. 138–183. MR 0383152
Lars Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183. MR 388463, DOI 10.1007/BF02392052
Kiyoshi Itô and Henry P. McKean Jr., Diffusion processes and their sample paths, Die Grundlehren der mathematischen Wissenschaften, Band 125, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-New York, 1965. MR 0199891
17. P. Lax, Lectures on hyperbolic equations, Stanford Lecture Notes, 1963.
Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
19. J. Lions and E. Magenes, Problèmes aux limites non homogènes et leurs applications, Dunod, Paris, 1967.
H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
Willard Miller Jr., Symmetry and separation of variables, Encyclopedia of Mathematics and its Applications, Vol. 4, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. With a foreword by Richard Askey. MR 0460751
Louis Nirenberg, Lectures on linear partial differential equations, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 17, American Mathematical Society, Providence, R.I., 1973. Expository Lectures from the CBMS Regional Conference held at the Texas Technological University, Lubbock, Tex., May 22–26, 1972. MR 0450755
Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR 0219861
24. M. Reed and B. Simon, Methods of mathematical physics, Academic Press, New York, Vol. I, 1975, Functional analysis, Vol. II, 1975, Fourier analysis and self adjointness, Vol. III, Scattering theory (to appear), Vol. IV, 1979, Spectral theory.
Mikio Sato, Takahiro Kawai, and Masaki Kashiwara, Microfunctions and pseudo-differential equations, Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata, 1971; dedicated to the memory of André Martineau), Lecture Notes in Math., Vol. 287, Springer, Berlin, 1973, pp. 265–529. MR 0420735
Martin Schechter, Spectra of partial differential operators, 2nd ed., North-Holland Series in Applied Mathematics and Mechanics, vol. 14, North-Holland Publishing Co., Amsterdam, 1986. MR 869254
27. E. Stein, Singular integral operators and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970.
Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
29. K. Yosida, Functional analysis, Springer-Verlag, New York, 1965.
- 1.
- S. Agmon, Lectures on elliptic boundary value problems, Van Nostrand, New York, 1964. MR 0178246
- 2.
- S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions, Comm. Pure Appl. Math. 12 (1959), 623-727. MR 125307
- 3.
- L. Bers, F. John, and M. Schechter, Partial differential equations, Wiley, New York, 1964. MR 162045
- 4.
- R. Courant and D. Hilbert, Methods of mathematical physics. II, Wiley, New York, 1966. MR 195654
- 5.
- J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-259. MR 388464
- 6.
- Y. V. Egorov, On canonical transformations of pseudodifferential equations, Uspehi Mat. Nauk 25 (1969), 235-236.
- 7.
- L. Ehrenpreis, Fourier analysis in the complex domain, Wiley, New York, 1970.
- 8.
- A. Friedman, Partial differential equations, Holt, Rinehart and Winston, New York, 1969. MR 445088
- 9.
- A. Friedman, Stochastic differential equations and applications. I, II, Academic Press, New York, 1975. MR 494490
- 10.
- G. Folland and E. Stein, Estimates for the $\bar \partial \sbb$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. MR 367477
- 11.
- P. Garabedian, Partial differential equations, Wiley, New York, 1964. MR 162045
- 12.
- D. Gilbarg and N. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, New York, 1977. MR 473443
- 13.
- L. Hörmander, Linear partial differential operators, Springer-Verlag, New York, 1964. MR 248435
- 14.
- L. Hörmander, Pseudo-differential operators and hypoelliptic equations, singular integrals, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1967, pp. 138-183. MR 383152
- 15.
- L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183. MR 388463
- 16.
- K. Ito and H. McKean, Diffusion processes and their sample paths, Springer-Verlag, New York, 1965. MR 199891
- 17.
- P. Lax, Lectures on hyperbolic equations, Stanford Lecture Notes, 1963.
- 18.
- P. Lax and R. Phillips, Scattering theory, Academic Press, New York, 1967. MR 217440
- 19.
- J. Lions and E. Magenes, Problèmes aux limites non homogènes et leurs applications, Dunod, Paris, 1967.
- 20.
- H. McKean, Stochastic integrals, Academic Press, New York, 1969. MR 247684
- 21.
- W. Miller, Jr., Symmetry and separation of variables, Encyclopedia of Math. and its Applications, vol. 4, Addison-Wesley, Reading, Mass., 1977. MR 460751
- 22.
- L. Nirenberg, Lectures on linear partial differential equations, CBMS Regional Conf. Ser. in Math., no. 17, Amer. Math. Soc., Providence, R. I., 1973, pp. 1-46. MR 450755
- 23.
- M. Protter and H. Weinberger, Maximum principles in differential equations, Prentice-Hall, Englewood Cliffs, N. J., 1967. MR 219861
- 24.
- M. Reed and B. Simon, Methods of mathematical physics, Academic Press, New York, Vol. I, 1975, Functional analysis, Vol. II, 1975, Fourier analysis and self adjointness, Vol. III, Scattering theory (to appear), Vol. IV, 1979, Spectral theory.
- 25.
- M. Sato, T. Kawai, and M. Kashiwara, Microfunctions and pseudo differential equations, Lecture Notes in Math., vol. 287, Springer-Verlag, New York, 1973, pp. 265-529. MR 420735
- 26.
- M. Schechter, Spectra of partial differential operators, North-Holland, Amsterdam, 1971. MR 869254
- 27.
- E. Stein, Singular integral operators and differentiability properties of functions, Princeton Univ. Press, Princeton, N. J., 1970.
- 28.
- E. Stein, and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, Princeton, N. J., 1971. MR 304972
- 29.
- K. Yosida, Functional analysis, Springer-Verlag, New York, 1965.
Review Information:
Reviewer:
Michael E. Taylor
Journal:
Bull. Amer. Math. Soc.
1 (1979), 661-667
DOI:
https://doi.org/10.1090/S0273-0979-1979-14653-6
