L’objet du mémoire est l’extension des propriétés classiques des espaces de Banach à deux catégories d’espaces plus vastes, qui interviennent de manière essentielle dans la théorie des Distributions : les espaces
@article{AIF_1949__1__61_0, author = {Dieudonn\'e, Jean and Schwartz, Laurent}, title = {La dualit\'e dans les espaces $({\mathcal {F}})$ et $({\mathcal {L}}{\mathcal {F}})$}, journal = {Annales de l'Institut Fourier}, pages = {61--101}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {1}, year = {1949}, doi = {10.5802/aif.8}, mrnumber = {12,417d}, zbl = {0035.35501}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.8/} }
TY - JOUR AU - Dieudonné, Jean AU - Schwartz, Laurent TI - La dualité dans les espaces $({\mathcal {F}})$ et $({\mathcal {L}}{\mathcal {F}})$ JO - Annales de l'Institut Fourier PY - 1949 SP - 61 EP - 101 VL - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.8/ DO - 10.5802/aif.8 LA - fr ID - AIF_1949__1__61_0 ER -
%0 Journal Article %A Dieudonné, Jean %A Schwartz, Laurent %T La dualité dans les espaces $({\mathcal {F}})$ et $({\mathcal {L}}{\mathcal {F}})$ %J Annales de l'Institut Fourier %D 1949 %P 61-101 %V 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.8/ %R 10.5802/aif.8 %G fr %F AIF_1949__1__61_0
Dieudonné, Jean; Schwartz, Laurent. La dualité dans les espaces $({\mathcal {F}})$ et $({\mathcal {L}}{\mathcal {F}})$. Annales de l'Institut Fourier, Tome 1 (1949), pp. 61-101. doi : 10.5802/aif.8. http://www.numdam.org/articles/10.5802/aif.8/
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- Ouverts concaves et théorèmes de dualité pour les systèmes différentiels à coefficients constants, Commentarii Mathematici Helvetici, Volume 46 (1971) no. 1, p. 487 | DOI:10.1007/bf02566861
- Nonexistence of a continuous right inverse for surjective linear partial differential operators on the Fréchet spaces
, Journal of Differential Equations, Volume 10 (1971), pp. 291-313 | DOI:10.1016/0022-0396(71)90053-2 | Zbl:0215.49202 - Fredholm Operators and Their Generalizations, Mathematical Analysis (1971), p. 37 | DOI:10.1007/978-1-4757-1589-7_2
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spaces and distributions on compact groups, and spectral synthesis on , Mathematische Annalen, Volume 194 (1971), pp. 52-67 | DOI:10.1007/bf01351822 | Zbl:0207.43701 - Systems of division problems for distributions, Transactions of the American Mathematical Society, Volume 155 (1971), pp. 493-504 | DOI:10.2307/1995699 | Zbl:0213.40101
- (LF)-spaces with absolute bases, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 67 (1970) no. 2, p. 283 | DOI:10.1017/s0305004100045564
- An Introduction to Distributions, The American Mathematical Monthly, Volume 77 (1970) no. 3, p. 227 | DOI:10.1080/00029890.1970.11992462
- Applications of Distributions to Pde Theory, The American Mathematical Monthly, Volume 77 (1970) no. 3, p. 241 | DOI:10.1080/00029890.1970.11992463
- Finitely generated ideals of differentiable functions, Transactions of the American Mathematical Society, Volume 150 (1970), pp. 213-225 | DOI:10.2307/1995491 | Zbl:0199.46301
- Nilpotent locally convex Lie algebras and Lie field structures, Communications in Mathematical Physics, Volume 14 (1969) no. 2, p. 89 | DOI:10.1007/bf01645132
- Das Spektrum der stetigen Endomorphismen von ψ, Mathematische Annalen, Volume 181 (1969) no. 4, p. 297 | DOI:10.1007/bf01350669
- Sur les ultradistributions, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, Volume 1 (1968) no. 3, pp. 395-415 | DOI:10.24033/asens.1167 | Zbl:0164.15401
- Characterization of separability for LF-spaces, Annales de l'Institut Fourier, Volume 18 (1968) no. 2, pp. 87-90 | DOI:10.5802/aif.293 | Zbl:0174.43801
- Nukleare Räume, Einführung in die Theorie der lokalkonvexen Räume, Volume 56 (1968), p. 148 | DOI:10.1007/bfb0098576
- BIBLIOGRAPHY, Spaces of Fundamental and Generalized Functions (1968), p. 257 | DOI:10.1016/b978-1-4832-2977-5.50010-7
- Appendix: The Borel Graph Theorem, Volume 25 (1967), p. 549 | DOI:10.1016/s0079-8169(08)60302-5
- Processus linéaires, processus généralisés, Annales de l'Institut Fourier, Volume 17 (1967) no. 1, pp. 1-92 | DOI:10.5802/aif.249 | Zbl:0167.16702
- Quelques questions d'espaces vectoriels topologiques, Commentarii Mathematici Helvetici, Volume 42 (1967) no. 1, p. 314 | DOI:10.1007/bf02564425
- Stability of bases in complete barrelled spaces, Proceedings of the American Mathematical Society, Volume 18 (1967), pp. 1045-1050 | DOI:10.2307/2035792 | Zbl:0161.10302
- On the solvability of one class of differential equations of infinite order, Soviet Mathematical Journal, Volume 8 (1967) no. 6, p. 1004 | DOI:10.1007/bf02196408
- Étude des fonctions quasi-stationnaires et de leurs applications aux équations différentielles opérationnelles, Bulletin de la Société Mathématique de France. Supplément. Mémoires, Volume 6 (1966), p. 175 | Zbl:0165.49504
- Espaces de fonctions et distributions du type de Gevrey et problèmes aux limites paraboliques, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 68 (1965), pp. 341-417 | DOI:10.1007/bf02411029 | Zbl:0138.08401
- Bipositive and Isometric Isomorphisms of Some Convolution Algebras, Canadian Journal of Mathematics, Volume 17 (1965), p. 839 | DOI:10.4153/cjm-1965-082-8
- Espaces Localement K-Convexes. III, Indagationes Mathematicae (Proceedings), Volume 68 (1965), p. 273 | DOI:10.1016/s1385-7258(65)50032-9
- Operatoren verallgemeinerter Funktionen, Mathematische Annalen, Volume 158 (1965) no. 4, p. 215 | DOI:10.1007/bf01360041
- Operatorenrechnung auf funktionalanalytischer Grundlage, Mathematische Zeitschrift, Volume 88 (1965) no. 1, p. 1 | DOI:10.1007/bf01112690
- Carleman estimates for the laplace-beltrami equation on complex manifolds, Publications mathématiques de l'IHÉS, Volume 25 (1965) no. 1, p. 81 | DOI:10.1007/bf02684398
- Sur certains aspects des problèmes aux limites non homogenes pour des opérateurs paraboliques, Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser, Volume 18 (1964), pp. 303-344 | Zbl:0138.08302
- Sous-espaces d'espaces vectoriels topologiques et noyaux associés. (Noyaux reproduisants.), Journal d'Analyse Mathématique, Volume 13 (1964), pp. 115-256 | DOI:10.1007/bf02786620 | Zbl:0124.06504
- Problèmes aux limites non homogenes. VII, Annali di Matematica Pura ed Applicata. Serie Quarta, Volume 63 (1963), pp. 201-224 | DOI:10.1007/bf02412183 | Zbl:0126.31103
- A generalization of two-norm spaces, Arkiv för Matematik, Volume 5 (1963) no. 1-2, p. 27 | DOI:10.1007/bf02591112
- On the continuity of inverse operators in (LF)-spaces, Bulletin of the American Mathematical Society, Volume 69 (1963), pp. 832-834 | DOI:10.1090/s0002-9904-1963-11053-8 | Zbl:0121.09903
- Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, Journal d'Analyse Mathématique, Volume 11 (1963), pp. 1-164 | DOI:10.1007/bf02789982 | Zbl:0124.31804
- Su alcuni esempi notevoli di dualit*a2 fra spazi lineari topologici, Rendiconti del Seminario Matemàtico e Fisico di Milano, Volume 33 (1963), pp. 102-113 | DOI:10.1007/bf02923238 | Zbl:0187.37802
- Sur l'approximation par distributions à support discret, Annales Scientifiques de l'École Normale Supérieure. Troisième Série, Volume 79 (1962), pp. 71-91 | DOI:10.24033/asens.1107 | Zbl:0107.09104
- Introduction de poids dans l'étude de problèmes aux limites, Annales de l'Institut Fourier, Volume 12 (1962), pp. 299-414 | DOI:10.5802/aif.124 | Zbl:0112.33903
- On a space of distributions with support in a closed subset, Hiroshima Mathematical Journal, Volume 26 (1962) no. 1 | DOI:10.32917/hmj/1206139770
- On structure of the algebra of field operators, Il Nuovo Cimento, Volume 24 (1962) no. 2, p. 214 | DOI:10.1007/bf02745645
- Functional analysis and partial differential equations. II, Mathematische Annalen, Volume 145 (1962), pp. 81-226 | DOI:10.1007/bf01342796 | Zbl:0103.31602
- Locally convex spaces with theB(?)-property, Mathematische Annalen, Volume 146 (1962) no. 5, p. 413 | DOI:10.1007/bf01470654
- Barrelled spaces and the open mapping theorem, Proceedings of the American Mathematical Society, Volume 13 (1962) no. 3, p. 423 | DOI:10.1090/s0002-9939-1962-0150573-8
- Distributions sur un groupe localement compact et applications à l'étude des représentations des groupes
-adiques, Bulletin de la Société Mathématique de France, Volume 89 (1961), pp. 43-75 | DOI:10.24033/bsmf.1559 | Zbl:0128.35701 - On fully complete spaces, Tôhoku Mathematical Journal. Second Series, Volume 13 (1961), pp. 485-490 | DOI:10.2748/tmj/1178244251 | Zbl:0111.10804
- Sur quelques extensions de la notion de distribution, Annales Scientifiques de l'École Normale Supérieure. Troisième Série, Volume 77 (1960), pp. 41-121 | DOI:10.24033/asens.1087 | Zbl:0104.33403
- On the state of a linear operator and its adjoint, Mathematische Annalen, Volume 141 (1960), pp. 153-160 | DOI:10.1007/bf01360169 | Zbl:0096.08502
- Opérateurs différentiels hypoelliptiques, Annales de l'Institut Fourier, Volume 9 (1959), pp. 1-73 | DOI:10.5802/aif.85 | Zbl:0197.36602
- Functional analysis and partial differential equations. I, Mathematische Annalen, Volume 138 (1959), pp. 55-79 | DOI:10.1007/bf01369666 | Zbl:0086.10301
- Théorie des distributions à valeurs vectorielles. II, Annales de l'Institut Fourier, Volume 8 (1958), pp. 1-209 | DOI:10.5802/aif.77 | Zbl:0089.09801
- Halbgeordnete lokalkonvexe Vektorräume, Mathematische Annalen, Volume 135 (1958), pp. 115-141 | DOI:10.1007/bf01343098 | Zbl:0080.31501
- Théorie des distributions à valeurs vectorielles, Annales de l'Institut Fourier, Volume 7 (1957), pp. 1-141 | DOI:10.5802/aif.68 | Zbl:0089.09601
- Sur une classe d'opérateurs différentiels hypoelliptiques, Bulletin de la Société Mathématique de France, Volume 85 (1957), pp. 283-306 | DOI:10.24033/bsmf.1490 | Zbl:0082.09303
- Zur Theorie der Markoffschen Prozesse, Mathematische Annalen, Volume 133 (1957), pp. 375-399 | DOI:10.1007/bf01343752 | Zbl:0078.32102
- Generalized random variables, Transactions of the American Mathematical Society, Volume 84 (1957), pp. 273-309 | DOI:10.2307/1992815 | Zbl:0078.31003
- On the second dual of the space of continuous functions, Transactions of the American Mathematical Society, Volume 86 (1957), pp. 70-90 | DOI:10.2307/1992866 | Zbl:0081.10903
- Fonctions croissantes et mesures sur les espaces topologiques ordonnes, Annales de l'Institut Fourier, Volume 6 (1956), pp. 187-269 | DOI:10.5802/aif.64 | Zbl:0074.28201
- Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution, Annales de l'Institut Fourier, Volume 6 (1956), pp. 271-355 | DOI:10.5802/aif.65 | Zbl:0071.09002
- La théorie de Fredholm, Bulletin de la Société Mathématique de France, Volume 84 (1956), pp. 319-384 | DOI:10.24033/bsmf.1476 | Zbl:0073.10101
- Sur les représentations induites des groupes de Lie, Bulletin de la Société Mathématique de France, Volume 84 (1956), pp. 97-205 | DOI:10.24033/bsmf.1469 | Zbl:0074.10303
- Ergodentheorie und fastperiodische Funktionen auf Halbgruppen, Mathematische Zeitschrift, Volume 64 (1956), pp. 298-338 | DOI:10.1007/bf01166575 | Zbl:0070.11701
- On The Closed Graph Theorem, Proceedings of the Glasgow Mathematical Association, Volume 3 (1956) no. 1, p. 9 | DOI:10.1017/s2040618500033372
- Une Caracterisation Vectorielle-Metrique Des Espaces L1, Canadian Journal of Mathematics, Volume 7 (1955), p. 552 | DOI:10.4153/cjm-1955-060-6
- Bounded Representations on a Topological Vector Space and Weak Almost Periodicity, Japanese journal of mathematics :transactions and abstracts, Volume 25 (1955) no. 0, p. 21 | DOI:10.4099/jjm1924.25.0_21
- Espaces de fonctions différentiables à valeurs vectorielles, Journal d'Analyse Mathématique, Volume 4 (1955), pp. 88-148 | DOI:10.1007/bf02787718 | Zbl:0066.09601
- Über das Spektrum der Endomorphismen eines linearen Raumes, Mathematische Nachrichten, Volume 13 (1955), pp. 1-8 | DOI:10.1002/mana.19550130102 | Zbl:0064.10903
- Pseudonormen in der Theorie der linearen topologischen Räume, Mathematische Nachrichten, Volume 14 (1955), pp. 29-38 | DOI:10.1002/mana.19550140106 | Zbl:0065.34402
- Completeness and compactness in linear topological spaces, Transactions of the American Mathematical Society, Volume 79 (1955), pp. 256-280 | DOI:10.2307/1992847 | Zbl:0064.35502
- A theory of Radon measures on locally compact spaces, Acta Mathematica, Volume 89 (1953), pp. 133-164 | DOI:10.1007/bf02393005 | Zbl:0050.05702
- Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du Type C(K), Canadian Journal of Mathematics, Volume 5 (1953), p. 129 | DOI:10.4153/cjm-1953-017-4
- Sur les espaces de solutions d'une classe générale d'équations aux dérivées partielles, Journal d'Analyse Mathématique, Volume 2 (1953), pp. 243-280 | DOI:10.1007/bf02825639 | Zbl:0051.08801
- Bounded-weak topologies and completeness in vector spaces, Mathematical Proceedings of the Cambridge Philosophical Society, Volume 49 (1953) no. 2, p. 183 | DOI:10.1017/s0305004100028267
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-Räume in der Funktionentheorie. II, Mathematische Zeitschrift, Volume 58 (1953), pp. 414-435 | DOI:10.1007/bf01174156 | Zbl:0053.04404 - Randverteilungen analytischer Funktionen und Distributionen, Mathematische Zeitschrift, Volume 59 (1953) no. 1, p. 61 | DOI:10.1007/bf01180242
- On the representation of analytic functions by infinite series, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 245 (1953) no. 900, p. 429 | DOI:10.1098/rsta.1953.0003
- Summary of essential results in the theory of topological tensor products and nuclear spaces., Annales de l'Institut Fourier, Volume 4 (1952), pp. 73-112 | DOI:10.5802/aif.46 | Zbl:0055.09705
- Sur un théorème de Šmulian, Archiv der Mathematik, Volume 3 (1952), pp. 436-440 | DOI:10.1007/bf01900559 | Zbl:0048.08604
- �ber Stetigkeit von Integraltransformationen, Mathematische Zeitschrift, Volume 55 (1952) no. 2, p. 167 | DOI:10.1007/bf01268652
- Die Randverteilungen analytischer Funktionen, Mathematische Zeitschrift, Volume 57 (1952), pp. 13-33 | DOI:10.1007/bf01192913 | Zbl:0047.35203
- On the symmetry and bounded closure of locally convex spaces, Transactions of the American Mathematical Society, Volume 73 (1952), pp. 321-344 | DOI:10.2307/1990672 | Zbl:0047.10601
- Sur les espaces de Köthe, Journal d'Analyse Mathématique, Volume 1 (1951), pp. 81-115 | DOI:10.1007/bf02790084 | Zbl:0044.11703
- Neubegründung der Theorie der vollkommenen Räume, Mathematische Nachrichten, Volume 4 (1951), pp. 70-80 | DOI:10.1002/mana.19500040109 | Zbl:0042.11602
- Sur certains espaces vectoriels topologiques, Annales de l'Institut Fourier, Volume 2 (1950), pp. 5-16 | DOI:10.5802/aif.16 | Zbl:0042.35302
- Neubegründung der Theorie der vollkommenen Räume. Herrn Erhard Schmidt zuiri 75. Geburtstag gewidmet, Mathematische Nachrichten, Volume 4 (1950) no. 1-6, p. 70 | DOI:10.1002/mana.3210040109
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