Book Review
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MathSciNet review:
1567941
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Book Information:
Authors:
Richard D. Carmichael and
Dragiša Mitrović
Title:
Distributions and analytic functions
Additional book information:
Pitman Research Notes in Mathematics Series, vol. 206, Longman Scientific & Technical, Harlow, England. ISBN 0-582-01856-0; John Wiley &Sons, New York, (USA only), 1989, xii+347 pp., $42.00. ISBN 0-470-21398-5.
A. Cerezo, J. Chazarain, and A. Piriou, Introduction aux hyperfonctions, Hyperfunctions and theoretical physics (Rencontre, Nice, 1973; dédié à la mémoire de A. Martineau), Lecture Notes in Math., Vol. 449, Springer, Berlin, 1975, pp. 1–53 (French). MR 0394189
Leon Ehrenpreis, Solution of some problems of division. I. Division by a polynomial of derivation, Amer. J. Math. 76 (1954), 883–903. MR 68123, DOI 10.2307/2372662
L. Fantappié, Teoría de los Funcionales Analíticos y sus Aplicaciones, Consejo Superior de Investigaciones Científicas, Barcelona, 1943 (Spanish). MR 0014598
Alexandre Grothendieck, Sur certains espaces de fonctions holomorphes. I, J. Reine Angew. Math. 192 (1953), 35–64 (French). MR 58865, DOI 10.1515/crll.1953.192.35
Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
Masaki Kashiwara, Takahiro Kawai, and Tatsuo Kimura, Foundations of algebraic analysis, Princeton Mathematical Series, vol. 37, Princeton University Press, Princeton, NJ, 1986. Translated from the Japanese by Goro Kato. MR 855641
Adam Korányi, A Poisson integral for homogeneous wedge domains, J. Analyse Math. 14 (1965), 275–284. MR 179809, DOI 10.1007/BF02806394
Gottfried Köthe, Dualität in der Funktionentheorie, J. Reine Angew. Math. 191 (1953), 30–49 (German). MR 56824, DOI 10.1515/crll.1953.191.30
Gottfried Köthe, Die Randverteilungen analytischer Funktionen, Math. Z. 57 (1952), 13–33 (German). MR 52032, DOI 10.1007/BF01192913
Gottfried Köthe, J. Sebasti ao e Silva et l’analyse fonctionnelle, An. Fac. Ci. Univ. Porto 56 (1973), no. 4, 339–349. MR 0398743
Reinhold Meise, Representation of distributions and ultradistributions by holomorphic functions, Functional analysis: surveys and recent results (Proc. Conf., Paderborn, 1976) North-Holland Math. Studies, Vol. 27; Notas de Mat., No. 63, North-Holland, Amsterdam, 1977, pp. 189–208. MR 0482169
J. Sebastião e Silva, On the topology of analytic functional spaces, Univ. Lisboa Rev. Fac. Ci. A (2) 1 (1950), 23–102 (Portuguese, with French summary). MR 40576
13. C. L. da Silva Dias, Espaços vectoriais topológicos e sua aplicação nos espaços funcionais analiticos, Bol. Soc. Mat. São Paulo 5 (1950), 1-58.
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
Daniele C. Struppa, Luigi Fantappiè and the theory of analytic functionals, Italian mathematics between the two world wars (Italian) (Milan/Gargnano, 1986) Pitagora, Bologna, 1987, pp. 393–429 (Italian). MR 985785
Daniele C. Struppa and Cristina Turrini, Hyperfunctions and boundary values of holomorphic functions, Nieuw Arch. Wisk. (4) 4 (1986), no. 2, 91–118. MR 864474
- 1.
- A. Cerezo, J. Chazarain, and A. Piriou, Introduction aux hyperfonctions, Hyperfunctions and Theoretical Physics, Lecture Notes in Math., vol. 449, Springer-Verlag, Berlin, Heidelberg, New York, 1975, pp. 1-53. MR 0394189
- 2.
- L. Ehrenpreis, Solution of some problems of division, Amer. J. Math. 76 (1954), 883-903. MR 68123
- 3.
- L. Fantappiè, Teoría de los funcionales analíticos y sus aplicaciones, Consejo Superior de Investigaciones Cientificas, Barcelona, 1943. MR 14598
- 4.
- A. Grothendieck, Sur certains espaces de fonctions holomorphes, J. Reine Angew. Math. 192 (1953), 35-64; 77-95. MR 58865
- 5.
- L. Hörmander, The analysis of linear partial differential operators. I, Distribution Theory and Fourier Analysis, Grundlehren Math. Wiss., vol. 256, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. MR 717035
- 6.
- M. Kashiwara, T. Kawai, and T. Kimura, Foundations of algebraic analysis, Princeton Mathematical Series, vol. 37, Princeton Univ. Press, Princeton, NJ, 1986. MR 855641
- 7.
- A. Korányi, A Poisson integral for homogeneous wedge domains, J. Analyse Math. 14 (1965), 275-284. MR 179809
- 8.
- G. Köthe, Dualität in der Funktionentheorie, J. Reine Angew. Math. 191 (1953), 30-49. MR 56824
- 9.
- G. Köthe, Die Randverteilungen analytischer Funktionen, Math. Z. 57 (1952), 13-33. MR 52032
- 10.
- G. Köthe, J. Sebastião e Silva et l'analyse fonctionnelle, An. Fac. Ci. Univ. Porto 56 (1973), 339-349. MR 398743
- 11.
- R. Meise, Representation of distributions and ultradistributions by holomorphic functions, Functional Analysis: Surveys and Recent Results, North-Holland Mathematics Studies, vol. 27 (Proc. Conf., Paderborn, 1976) Notas de Mat., pp. 189-208; no. 63, North-Holland, Amsterdam, New York, Oxford, 1977. MR 482169
- 12.
- J. Sebastião e Silva, Sobre a topologia dos espaços funcionais analíticos, Revista Fac. Ci. Lisboa, II Ser., A Ci. Mat. 1 (1950), 23-102. MR 40576
- 13.
- C. L. da Silva Dias, Espaços vectoriais topológicos e sua aplicação nos espaços funcionais analiticos, Bol. Soc. Mat. São Paulo 5 (1950), 1-58.
- 14.
- E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, vol. 32, Princeton Univ. Press, Princeton, N. J., 1971. MR 304972
- 15.
- D. C. Struppa, Luigi Fantappiè e la teoria dei funzionali analitici, Proceedings of the Conference "La Matematica Italiana tra le due guerre mondiali", Milano-Gargnano, 1986, Pitagora, Bologna, 1987, pp. 393-429. MR 985785
- 16.
- D. C. Struppa and C. Turrini, Hyperfunctions and boundary values of holomorphic functions, Nieuw Arch. Wisk. 4 (1986), 91-118. MR 864474
Review Information:
Reviewer:
John Horváth
Journal:
Bull. Amer. Math. Soc.
25 (1991), 162-170
DOI:
https://doi.org/10.1090/S0273-0979-1991-16056-8