Bulletin of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-9485(e) ISSN 0273-0979(p)

A setting for global analysis

Author(s): James Eells Jr.
Journal: Bull. Amer. Math. Soc. 72 (1966), 751-807.
MathSciNet review: 0203742
Retrieve article in: PDF

References | Additional information

References:

1.: R. Abraham, Transversality in manifolds of mappings, Bull. Amer. Math. Soc. 69 (1963), 470-474. MR 149495
2.: R. Abraham, Lectures of Smale on differential topology, Notes at Columbia University, New York, 1962-1963.
3.: V. I. Anosov, Critical points of periodic functionals, Soviet Math. Dokl. 1 (1960), 208-210. MR 119115
4.: R. F. Arens and J. Eells, Jr., On embedding uniform and topological spaces, Pacific J. Math. 6 (1956), 397-403. MR 81458
5.: R. G. Bartle, On the openness and inversion of differentiable mappings, Ann. Acad. Sci. Fenn. 257 (1958), 3-8. MR 104172
6.: A. Bastiani, Applications différentiables et variétés différentiables de dimension infinie, J. Analyse Math. 13 (1964), 1-114. MR 177277
7.: I. Berstein, J. Eells, Jr. and K. Gęba, Poincaré duality in function spaces, (In preparation).
8.: C. Bessaga, Every infinite-dimensional Hilbert space is diffeomorphic with its unit sphere, Bull. Acad. Polon. Sci., (to appear). MR 193646
9.: G. Birkhoff, Analytical groups, Trans. Amer. Math. Soc. 43 (1938), 61-101. MR 1501934
10.: R. Bonic and J. Frampton, Differentiable functions on certain Banach spaces, Bull. Amer. Math. Soc. 71 (1965), 393-395. MR 172084
11.: R. Bonic and J. Frampton, Smooth functions on Banach manifolds, (to appear). MR 198492
12.: R. Bott, Lectures on K-theory, Mimeographed notes, Harvard University, Cambridge, Mass., 1962.
13.: N. Bourbaki, Espaces vectoriels topologiques, Hermann, Paris, 1953; Chapters I-II. Hermann, Paris, 1955; Chapters III-IV.
14.: H. J. Bremermann, Holomorphic functionals and complex convexity in Banach spaces, Pacific J. Math. 7 (1957), 811-831. MR 88709
15.: F. E. Browder, On a generalization of the Schauder fixed point theorem, Duke Math. J. 26 (1959), 291-304. MR 105629
16.: F. E. Browder, Infinite dimensional manifolds and nonlinear elliptic eigenvalue problems, Ann. of Math. 82 (1965), 459-477. MR 203249
17.: F. E. Browder, Fixed point theorems on infinite dimensional manifolds, Trans. Amer. Math. Soc. 119 (1965), 179-194. MR 195082
18.: I. Colojoară, On Whitney's imbedding theorem, Rev. Roumaine Math. Pures Appl. 10 (1965), 291-296. MR 182018
19.: P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematick, Vol. 33, Springer, Berlin, 1964. MR 176478
20.: H. H. Corson, Collections of convex sets which cover a Banach space, Fund. Math. 49 (1961), 143-145. MR 125430
21.: J. Cronin, Fixed points and topological degree in nonlinear analysis, Math. Surveys No. 11, Amer. Math. Soc., Providence, R. I., 1964. MR 164101
22.: J. A. Dieudonné, Recent developments in the theory of locally convex vector spaces, Bull. Amer. Math. Soc. 59 (1953), 495-512. MR 62334
23.: J. A. Dieudonné, Foundations of modern analysis, Academic Press, New York, 1960. MR 120319
24.: J. Dixmier and A. Douady, Champs continus d'espaces hilbertiens et de C*-algèbres, Bull. Soc. Math. France 91 (1963), 227-284. MR 163182; 24a. A. Douady, Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Sem. Collège de France, 1964-1965.
25.: J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367. MR 44116
26.: N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1958.
27.: E. Dynkin, Normed Lie algebras and analytic groups, Uspehi Mat. Nauk. 5 (1950), no. 1 (35) 135-186; Amer. Math. Soc. Transl. Vol. 97 (1953), 66 pp.
28.: C. J. Earle and J. Eells, Jr., Foliations and fibrations. On the differential geometry of Teichmüller spaces, (to appear). MR 215320
29.: J. Eells, Jr., On the geometry of function spaces, Symp. Inter. de Topologia Alg., Mexico, 1956; 1958, 303-308. MR 98419
30.: J. Eells, Jr., On submanifolds of certain function spaces, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1520-1522. MR 112148
31.: J. Eells, Jr., A class of smooth bundles over a manifold, Pacific J. Math. 10 (1960), 525-538. MR 120656
32.: J. Eells, Jr., Alexander-Pontrjagin duality in function spaces, Proc. Sympos. Pure Math. Vol. III, Amer. Math. Soc., Providence, R. I., 1961, 109-129. MR 125580
33.: J. Eells, Jr., Analysis on manifolds, Mimeographed notes, Cornell University, Ithaca, N. Y., 1964-1965.
34.: J. Eells, Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160. MR 164306
35.: J. Eells, Jr., Energie et déformations en géométrie différentielle, Ann. Inst. Fourier (Grenoble) 14 (1964), 61-69. MR 172310
36.: J. Eells, Jr., Variational theory in fibre bundles, Proc. Kyoto Conference on Differential Geometry, Kyoto, 1965.
37.: J. Frampton, Smooth partitions of unity on Banach manifolds, Ph.D. Thesis, Yale University, New Haven, Conn., 1965.
38.: K. Gęba, Sur les groupes de cohomotopie dans les espaces de Banach, C. R. Acad. Sci. Paris 254 (1962), 3293-3295. MR 139170
39.: K. Gęba, Algebraic topology methods in the theory of compact fields in Banach spaces, Fund. Math. 54 (1964), 177-209. MR 162117; 39a. K. Gęba and A. Granas, Algebraic topology in linear normed spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. I, 13 (1965), 287-290; II, 13 (1965), 341-346. MR 184235
40.: G. Glaeser, Étude de quelques algèbres tayloriennes, J. Analyse Math. 6 (1958), 1-125. MR 101294
41.: A. Granas, The theory of compact vector fields and some of its applications to topology of functional spaces. I, Rozprawy Mat. 30 (1962). MR 149253
42.: L. Graves, Riemann integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc. 29 (1927), 163-177. MR 1501382
43.: L. Graves, Implicit functions and differential equations in general analysis, Trans. Amer. Math. Soc. 29 (1927), 514-552. MR 1501403
44.: L. Graves, Topics in functional calculus, Bull. Amer. Math. Soc. 41 (1935), 641-662; 42 (1936), 381-382.
45.: L. Graves and T. Hildebrandt, Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. 29 (1927), 127-153. MR 1501380
46.: N. Grossman, Geodesics on Hilbert manifolds, Ph.D. Thesis, University of Minnesota, Minneapolis, Minn., 1964.
47.: N. Grossman, Hilbert manifolds without epiconjugate points, Mimeographed notes, Institute for Advanced Study, Princeton, N. J.
48.: M. Hestenes, Applications of the theory of quadratic forms in Hilbert space to the calculus of variations, Pacific J. Math. 1 (1951), 525-581. MR 46590
49.: M. Hestenes, Quadratic variational theory and linear elliptic partial differential equations, Trans. Amer. Math. Soc. 101 (1961), 306-350. MR 133575
50.: E. Hille and R. S. Phillips, Functional analysis and semigroups, Amer. Math. Soc. Colloq. Publ., Vol 31, Amer. Math. Soc., Providence, R. I., 1957. MR 89373
51.: L. Hörmander, Linear partial differential operators, Springer, Berlin, 1963. MR 404822
52.: K. Jänich, Vektorraumbündel und der Raum der Fredholm-Operatoren, Math. Ann. 161 (1965), 129-142. MR 190946
53.: S. Kakutani, Topological properties of the unit sphere in Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269-271. MR 14203
54.: H. H. Keller, Über die Differentialgleichung erster Ordnung in normierten linearen Räurmen, Rend. Circ. Mat. Palermo 8 (1959), 117-144. MR 121554
55.: M. Kerner, Abstract differential geometry, Compositio Math. 4 ( 1937), 308-341. MR 1556977
56.: V. L. Klee, Jr., Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 10-43. MR 54850
57.: V. L. Klee, Some topological properties of convex sets, Trans. Amer. Math. Soc. 78 (1955), 30-45. MR 69388
58.: W. Klingenberg, The theorem of the three closed geodesics, Bull. Amer. Math. Soc. 71 (1965), 601-605. MR 177374
59.: M. Klingmann, Doctoral Dissertation, University of Heidelberg, 1965.
60.: M. A. Krasnosel'skiĭ, Topological methods in the theory of non-linear integral equations, Macmillan, New York, 1964. Translated from the 1956 Russian edition. MR 96983
61.: N. H. Kuiper, The homotopy type of the unitary group of Hilbert space, Topology 3 (1965), 19-30. MR 179792
62.: I. Kupka, Counterexample to the Morse-Sard theorem in the case of infinite dimensional manifolds, Proc. Amer. Math. Soc. 16 (1965), 954-957. MR 182024
63.: J. Kurzweil, An approximation in real Banach spaces, Studia Math. 14 (1954), 214-231. MR 68732
64.: S. Lang, Introduction to differentiable manifolds, Interscience, New York, 1962. MR 155257
65.: D. Laugwitz, Differentialgeometrie ohne Dimensionsaxiom. I, II, Math. Z. 61 (1954), 100-118, 134-149.
66.: D. Laugwitz, Über unendliche kontinuierliche Gruppen. I, Math. Ann. 130 (1955-1956), 337-350; II, Bayer, Akad. Wiss. Math.-Nat. Kl. 1956, 261-286. MR 75535
67.: D. Laugwitz, Grundlagen für die Geometrie der unendlichdimensionalen Finslerräume, Ann. Math. Pura Appl. (4) 41 (1956), 21-41. MR 78732
68.: J. Lelong, Sur les groupes à un paramètre de transformations des variétés différentiables, J. Math. Pures Appl. 37 (1958), 269-278. MR 98415
69.: J. Leray, Sur les équations et les transformations, J. Math. Pures Appl. 24 (1945), 201-248. MR 15788
70.: J. Leray, La théorie des points fixes et ses applications en analyse, Proc. Internat. Congress, Cambridge, Mass., 1950, 202-208. Vol. 2, Amer. Math. Soc. Providence, R. I., 1952. MR 47318
71.: J. Leray, Théorie des points fixes: Indice total et nombre de Lefschetz, Bull. Soc. Math. France 87 (1959), 221-233. MR 143202
72.: J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. École Norm. Sup. 51 (1934), 45-78. MR 1509338
73.: P. Lévy, Leçons d'analyse fonctionnelle, Gauthiers-Villars, Paris, 1922.
74.: B. Maissen, Lie-Gruppen mit Banachräumen als Parameterräume, Acta Math. 108 (1962), 229-269. MR 142693
75.: J. H. McAlpin, Infinite dimensional manifolds and Morse theory, Ph.D. Thesis, Columbia University, New York, 1965.
76.: W. Meyer, Kritische Mannigfaltigkeiten in Hilbert-mannigfaltigkeiten, Doctoral Dissertation, University of Bonn, 1964.
77.: A. D. Michal, General differential geometries and related topics, Bull. Amer. Math. Soc. 45 (1939), 525-563. MR 172
78.: J. W. Milnor, On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), 272-280. MR 100267
79.: C. B. Morrey, Jr., Multiple integrals in the calculus of variations, Amer. Math. Soc. Colloq. Lectures, Amherst, Mass., 1964.
80.: C. B. Morrey, Jr. and J. Eells, Jr., A variational method in the theory of harmonic integrals. I, Ann. of Math. 63 (1956), 91-128. MR 87764
81.: M. Morse, Abstract variational theory, Memor. Sci. Math. 92 (1939)
82.: M. Morse, Recent advances in variational theory in the large, Proc. Internat. Congress Math., Cambridge, Mass., 1950, 143-156. MR 44758
83.: J. Moser, A new technique for the construction of solutions of nonlinear differential equations, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1824-1831. MR 132859
84.: F. J. Murray, On complementary manifolds and projections in spaces L, Trans. Amer. Math. Soc. 41 (1937), 138-152. MR 1501894
85.: S. B. Myers, Algebras of differentiable functions, Proc. Amer. Math. Soc. 5 (1954), 917-922. MR 65823
86.: M. Nagumo, Degree of mapping in convex linear topological spaces, Amer. J. Math. 73 (1951), 497-511. MR 42697
87.: I. Namioka, A duality in function spaces, Trans. Amer. Math. Soc. 115 (1965), 131-144. MR 202133
88.: G. Neubauer, Über den Index abgeschlossener Operatoren in Banachräumen, Math. Ann. 160 (1965), 93-130; II, Math. Ann. 162 (1965), 92-119. MR 192351
89.: R. S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299-340. MR 158410
90.: R. S. Palais, On the homotopy type of certain groups of operators, Topology 3 (1965), 271-279. MR 175130
91.: R. S. Palais, Lectures on the differential topology of infinite dimensional manifolds, Mimeographed notes, by S. Greenfield, Brandeis University, Waltham, Mass.; 1964-1965.
92.: R. S. Palais, Homotopy theory of infinite dimensional manifolds, Mimeographed notes, Brandeis University, Waltham, Mass.; Topology 5 (1966), 1-16. MR 189028
93.: R. S. Palais, Lusternik-Schnirelman theory on Ganach manifolds, Mimeographed notes, Brandeis University, Waltham, Mass.; Topology 5 (1966), 115-132. MR 259955
94.: R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165-172. MR 158411
95.: L. E. Pursell and M. E. Shanks, The Lie algebra of a smooth manifold, Proc. Amer. Math. Soc. 5 (1954), 468-472. MR 64764
96.: C. R. Putnam and A. Wintner, The orthogonal group in Hilbert space, Amer. J. Math. 74 (1952), 52-78. MR 45121
97.: G. Restrepo, Differentiable norms in Banach spaces, Bull. Amer. Math. Soc. 70 (1964), 413-414. MR 161129
98.: E. H. Rothe, Zur Theorie der topologichen Ordnung und der Vektorfelder in Banachschen Räumen, Compositio Math. 5 (1937-1938), 177-197. MR 1556993
99.: E. H. Rothe, Critical points and gradient fields of scalars in Hilbert space, Acta Math. 85 (1951), 73-98. MR 43387
100.: E. H. Rothe, Leray-Schauder index and Morse type numbers in Hilbert space, Ann. of Math. 55 (1952), 433-467; 58 (1953), 593-594. MR 49493
101.: E. H. Rothe, Gradient mappings, Bull. Amer. Math. Soc. 59 (1953), 5-19. MR 52681
102.: E. H. Rothe, Critical point theory in Hilbert space under general boundary conditions. J. Math. Anal., Appl. 11 (1965), 357-409. MR 190951
103.: H. L. Royden, Function algebras, Bull. Amer. Math. Soc. 69 (1963), 281-298. MR 149327
104.: A. Sard, Hausdorff measure of critical images on Banach manifolds, Amer. J. Math. 87 (1965), 158-174. MR 173748
105.: J. Schauder, Über den Zusammenhang zwischen der Eindeutigkeit und Lösbarkeit. . ., Math. Ann. 106 (1932), 661-721. MR 1512780
106.: J. Schauder, Invarianz des Gebietes in Funktionalräumen, Studia Math. 1 (1929), 123-139.
107.: J. T. Schwartz, Generalizing the Lusternik-Schnirelman theory of critical points, Comm. Pure Appl. Math. 17 (1964), 307-315. MR 166796
108.: J. T. Schwartz, Nonlinear functional analysis, Mimeographed notes, New York University, New York, 1963-1964.
109.: I. Segal, Differential operators in the manifold of solutions of a non-linear differential equation, J. Math Pures Appl. 44 (1965), 71-132. MR 192369
110.: S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. 80 (1964), 382-396. MR 165539
111.: S. Smale, An infinite dimensional version of Sard's theorem. Amer. J. Math. 87 (1965), 861-866. MR 185604
112.: S. L. Sobolev, Applications of functional analysis in mathematical physics, (English transl.) Transl. Math. Monographs, Vol. 7, Amer. Math. Soc. Providence, R. I., 1964. MR 165337
113.: E. H. Spanier, Duality and S-theory, Bull. Amer. Math. Soc. 62 (1956), 194-203. MR 85506
114.: N. E. Steenrod, The topology of fibre bundles, Princeton Univ. Press, Princeton, N. J., 1951. MR 39258
115.: A. S. Švarc, The homotopic topology of Banach spaces, Dokl. Akad. Nauk SSSR 154 (1964), 61-63 = Soviet Math. Dokl. 5 (1964), 57-59. MR 160095
116.: J. Tomiyama and M. Takesaki, Applications of fibre bundles to the certain class of C*-algebras, Tôhoku Math. J. 13 (1961), 498-522. MR 139025
117.: M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day, San Francisco, Calif. 1964. Translated from the 1956 Russian edition. MR 176364
118.: W. T. Van Est and T. J. Korthagen, Non-enlargible Lie algebras, Nederl. Akad. Wetensch. Proc. Ser. A. 26 (1964), 15-31. MR 160851
119.: L. Waelbroek, Le calcul symbolique dans les algèbres commutatives, J. Math. Pures Appl. 33 (1954), 147-186. MR 73953
120.: A. Wasserman, Morse theory for G-manifolds, Bull. Amer. Math. Soc. 71 (1965), 384-388. MR 174064
121.: R. Wood, Banach algebras and Bott periodicity, Topology 4 (1965), 371-389. MR 185598

Additional Information:

DOI: 10.1090/S0002-9904-1966-11558-6
PII: S 0002-9904(1966)11558-6

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|