Bulletin of the American Mathematical Society

Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: 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 pp., ISBN 0-306-11035-0, $110.00$

1.

N. I. Akheizer and I. M. Glazman, Theory of linear operators in Hilbert space, Volume I and II, Ungar, New York, 1963.

John Rozier Cannon and Ulrich Hornung (eds.), Inverse problems, Internationale Schriftenreihe zur Numerischen Mathematik [International Series of Numerical Mathematics], vol. 77, Birkhäuser Verlag, Basel, 1986. MR 902806, DOI 10.1007/978-3-0348-7014-6

3.

A. Carasso and A. P. Stone, eds., Improperly posed boundary value problems, Res. Notes Math., vol. 1, Pitman, London, 1975. MR 0470424

David Colton, Richard Ewing, and William Rundell (eds.), Inverse problems in partial differential equations, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. MR 1046425

Klaus Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985. MR 787404, DOI 10.1007/978-3-662-00547-7

Heinz W. Engl and C. W. Groetsch (eds.), Inverse and ill-posed problems, Notes and Reports in Mathematics in Science and Engineering, vol. 4, Academic Press, Inc., Boston, MA, 1987. Papers from the Alpine-U.S. Seminar held in Sankt Wolfgang, June 1986. MR 1020304

C. W. Groetsch, The theory of Tikhonov regularization for Fredholm equations of the first kind, Research Notes in Mathematics, vol. 105, Pitman (Advanced Publishing Program), Boston, MA, 1984. MR 742928

P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14

Frank Jones, Lebesgue integration on Euclidean space, Jones and Bartlett Publishers, Boston, MA, 1993. MR 1204268

10.

G. Klambauer, Real analysis, American Elsevier, New York, 1973.

R. J. Knops (ed.), Symposium on Non-Well-Posed Problems and Logarithmic Convexity, Lecture Notes in Mathematics, Vol. 316, Springer-Verlag, Berlin-New York, 1973. Held in Heriot-Watt University, Edinburgh, March 22–24, 1972. MR 0369869

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.

L. E. Payne, Improperly posed problems in partial differential equations, Regional Conference Series in Applied Mathematics, No. 22, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1975. MR 0463736

Tadasi Nakayama, On Frobeniusean algebras. I, Ann. of Math. (2) 40 (1939), 611–633. MR 16, DOI 10.2307/1968946

R. E. Showalter, Hilbert space methods for partial differential equations, Monographs and Studies in Mathematics, Vol. 1, Pitman, London-San Francisco, Calif.-Melbourne, 1977. MR 0477394

Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0098966

Andrei N. Tikhonov, A. S. Leonov, A. I. Prilepko, I. A. Vasin, V. A. Vatutin, and A. G. Yagola (eds.), Ill-posed problems in natural sciences, VSP, Utrecht; TVP Science Publishers, Moscow, 1992. MR 1219957

G. Milton Wing, A primer on integral equations of the first kind, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1991. The problem of deconvolution and unfolding; With the assistance of John D. Zahrt. MR 1135580, DOI 10.1137/1.9781611971675

Kôsaku Yosida, Functional analysis, 4th ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag, New York-Heidelberg, 1974. MR 0350358

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 0902806

3.

A. Carasso and A. P. Stone, eds., Improperly posed boundary value problems, Res. Notes Math., vol. 1, Pitman, London, 1975. MR 0470424

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 1046425

5.

K. Deimling, Nonlinear functional analysis, Springer-Verlag, New York, 1985. MR 0787404

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 1020304

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 0742928

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 1204268

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 0369869

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 0463736

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 0477394

17.

A. E. Taylor, Introduction to functional analysis, Wiley, New York, 1958. MR 0098966

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 1219957

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 1135580

20.

K. Yosida, Functional analysis, fourth ed., Springer-Verlag, New York, 1974. MR 0350358