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Book Review
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Book Information
Author(s):
M. M. Lavrentév and L. Ya. Savelév
Title:
Linear operators and ill-posed problems
Additional book information:
translated from Russian by Nanka Publishers, Moscow,
Consultants Bureau, Plenum Publishing Corporation, New York,
1995,
xii + 382,
$110.00,
0-306-11035-0
References:
- 1.
- N. I. Akheizer and I. M. Glazman, Theory of linear operators in Hilbert space, Volume I and II, Ungar, New York, 1963.
- 2.
- J. R. Cannon and U. Hornung, eds., Inverse problems, Internat. Ser. Numer. Math., vol. 77, Birkhäuser-Verlag, Basel, 1986. MR 88c:00010
- 3.
- A. Carasso and A. P. Stone, eds., Improperly posed boundary value problems, Res. Notes Math., vol. 1, Pitman, London, 1975. MR 57:10178
- 4.
- D. Colton, R. Ewing, and W. Rundell, eds., Inverse problems in partial differential equations, SIAM Proc. Ser., Society for Industrial and Applied Mathematics, Philadelphia, 1990. MR 90j:35001
- 5.
- K. Deimling, Nonlinear functional analysis, Springer-Verlag, New York, 1985. MR 86j:47001
- 6.
- H. W. Engl and C. W. Groetsch, eds., Inverse and ill-posed problems, Notes Rep. Math. Sci. Engrg., vol. 4, Academic Press, Boston, 1987.MR 90f:00004
- 7.
- C. W. Groetsch, The theory of Tikhonov regularization for Fredholm equations of the first kind, Res. Notes Math., vol. 105, Pitman, London, 1984.MR 85k:45020
- 8.
- J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Dover, New York, 1952. MR 14:474f
- 9.
- F. Jones, Lebesgue integration on Euclidean space, Jones and Bartlett, Boston, 1993. MR 93m:28001
- 10.
- G. Klambauer, Real analysis, American Elsevier, New York, 1973.
- 11.
- R. J. Knops, ed., Symposium on non-well-posed problems and logarithmic convexity, Lecture Notes Math., vol. 316, Springer-Verlag, New York, 1973. MR 51:6098
- 12.
- M. M. Lavrentév, Some improperly posed problems of mathematical physics, Springer Tracts Nat. Philos., vol. II, Springer-Verlag, New York, 1967.
- 13.
- M. M. Lavrentév, V. G. Romanov, and S. P. Sisatskij, Problemi non ben posti in Fisica Matematica e Analisi, Consiglio Nazionale delle Ricerche, Publicazioni dell'Istituto di Analisi Globale e Applicazioni, Serie ``Problemi non ben posti ed inverse'', no. 12, Firenze, 1983.
- 14.
- L. E. Payne, Improperly posed problems in partial differential equations, Regional Conf. Ser. Appl. Math., vol. 22, Society for Industrial and Applied Mathematics, Philadelphia, 1975. MR 57:3678
- 15.
- I. G. Petrovsky, Lectures on partial differential equations, Interscience, New York, 1954. MR 16:478f
- 16.
- R. E. Showalter, Hilbert space methods for partial differential equations, Monographs Stud. Math., Pitman, London, 1977. MR 57:16922
- 17.
- A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1958. MR 20:5411
- 18.
- A. N. Tikhonov, editor-in-chief, Ill-posed problems in natural sciences, Proceedings of the International Conference, Ultrecht: VSP-The Netherlands/TSP Science, Moscow, 1992. MR 93m:00041
- 19.
- G. M. Wing (with assistance from J. D. Zahrt), A primer on integral equations of the first kind: The problem of deconvolution and unfolding, Society for Industrial and Applied Mathematics, Philadelphia, 1991. MR 93d:45001
- 20.
- K. Yosida, Functional analysis, fourth ed., Springer-Verlag, New York, 1974. MR 50:2851
Additional Information:
Reviewer(s):
John
R.
Cannon
Affiliation:
University of Central Florida
Email:
jcannon@pegasus.cc.ucf.edu
Review Information:
Journal:
Bull. Amer. Math. Soc.
34
(1997),
193-196.
MSC
(1991):
Primary 35R30, 35R25, 46E20, 47A50, 28A25
DOI:
10.1090/S0273-0979-97-00709-X
PII:
S 0273-0979(97)00709-X
Copyright of article:
Copyright
1997,
American Mathematical Society
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