<< . .

. 95
( : 97)



. . >>

Fourier Integral operators on a Riemannian manifold, Tokyo J. Math. 4 (1981a), 221“253.
Omori, H.; Maeda, Y.; Yoshioka, A., On regular Fr´chet Lie groups III, Tokyo J. Math. 4 (1981b),
e
255“277.
Omori, H.; Maeda, Y.; Yoshioka, A., On regular Fr´chet Lie groups IV. De¬nitions and funda-
e
mental theorems, Tokyo J. Math. 5 (1982), 365“398.
Omori, H.; Maeda, Y.; Yoshioka, A., On regular Fr´chet Lie groups V. Several basic properties,
e
Tokyo J. Math. 6 (1983), 39“64.
Omori, H.; Maeda, Y.; Yoshioka, A.; Kobayashi, O., On regular Fr´chet Lie groups VI. In¬nite
e
dimensional Lie groups which appear in general relativity, Tokyo J. Math. 6 (1983), 217“246.
Onishchik, A.L., On the classi¬cation of ¬ber spaces, Sov. Math. Dokl. 2 (1961), 1561“1564.
Onishchik, A.L., Connections with zero curvature and the de Rham theorem, Sov. Math. Dokl. 5
(1964), 1654“1657.
Onishchik, A.L., Some concepts and applications of non-abelian cohomology theory, Trans. Mosc.
Math. Soc. 17 (1967), 49“98.
Orihuela, J.; Valdivia, M., Projective generators and resolutions of identity in Banach spaces,
Rev. Mat. Univ. Complutense Madrid 2 (1989), 179“199.
Ovsienko, V.Y; Khesin, B.A., Korteweg“de Vrieß superequations as an Euler equation, Funct.
Anal. Appl. 21 (1987), 329“331.
Palais, R., Foundations of global non-linear analysis, Benjamin, New York, 1968.
Palais, R.S.; Terng, C.L., Critical point theory and submanifold geometry, Lecture Notes in Math-
ematics 1353, Springer-Verlag, Berlin, 1988.
Phelps, R.R., Convex functions, monotone operators and di¬erentiability, Lecture Notes in Math.
1364, Springer-Verlag, New York, 1989.
Pierpont, J., Theory of functions of real variables, Vol. 1, Boston, 1905.
Pisanelli, D., Applications analytiques en dimension in¬nie, C. R. Acad. Sci. Paris 274 (1972a),
760“762.
Pisanelli, D., Applications analytiques en dimension in¬nie, Bull. Sci. Math. 96 (1972b), 181“191.
Preiss, D., Gˆteaux di¬erentiable functions are somewhere Fr´chet di¬erentiable, Rend. Circ.
a e
Mat. Pal. 33 (1984), 122“133.
608 References

Preiss, D., Di¬erentiability of Lipschitz functions on Banach spaces, J. Funct. Anal. 91 (1990),
312“345.
Pressley, A.; Segal, G., Loop groups, Oxford Mathematical Monographs, Oxford University Press,
1986.
Procesi, C., Positive symmetric functions, Adv. Math. 29 (1978), 219“225.
Quinn, F., Ends III, J. Di¬er. Geo. 17 (1982), 503“521.
¨
Rademacher, H., Uber partielle und totale Di¬erenzierbarkeit von Funktionen mehrerer Variablen
und uber die Transformation der Doppelintegrale, Math. Ann. 79 (1919).
¨
Ramadas, T.R., On the space of maps inducing isomorphic connections, Ann. Inst. Fourier 32
(1982), 263“276.
Rao, M.M., Characterisation of Hilbert spaces by smoothness, Nederl. Akad. v. W. 71 (1967),
132“135.
Ratiu, T.; Schmid, R., The di¬erentiable structure of three remarkable di¬eomorphism groups,
Math. Z. 177 (1981), 81“100.
Rellich, F., St¨rungstheorie der Spektralzerlegung, I, Math. Ann. 113 (1937), 600“619.
o
Rellich, F., St¨rungstheorie der Spektralzerlegung, V, Math. Ann. 118 (1940), 462“484.
o
Rellich, F., Perturbation theory of eigenvalue problems, Lecture Notes, New York University,
1953; Gordon and Breach, New York, London, Paris, 1969.
Restrepo, G., Di¬erentiable norms in Banach spaces, Bull. Am. Math. Soc. 70 (1964), 413“414.
Restrepo, G., Di¬erentiable norms, Bol. Soc. Mat. Mex. 10 (1965), 47“55.
Riemann, B., Ueber die Hypothesen, welche der Geometrie zu Grunde liegen, Habilitationsvortrag
10. Juni 1854, Gesammelte Werke (H. Weber, ed.), Teubner, Leipzig, 1876.
Schaefer, H.H., Topological vector spaces, GTM 3, Springer-Verlag, New York, 1971.
Schichl, H., On the existence of slice theorems for moduli spaces on ¬ber bundles, Doctoral dis-
sertation, Univ. Wien, 1997.
Schla¬‚i, R, Universal connections, Invent. Math. 59 (1980), 59“65.
Schmidt, H.-J., The metric in the superspace of Riemannian metrics and its relation to gravity,
Di¬erential Geometry and its Applications, Brno, Csechoslovakia, 1989, World Scienti¬c,
Singapur, 1990, pp. 405“411.
Sebasti˜o e Silva, J., As fun¸˜es anal´
a co iticas e a an´lise funcional, Dissertation, 1948.
a
Sebasti˜o e Silva, J., As fun¸˜es anal´
a co iticas e a an´lise funcional, Port. Math. 9 (1950a), 1“130.
a
Sebasti˜o e Silva, J., Sobre a topologia dos espa¸os funcionais anal´
a c iticos, Rev. Fac. Cienc. Lisboa,
ser. A1 2 (1950b), 23“102.
Sebasti˜o e Silva, J., Sui fondamenti della teoria dei funzionali analitici, Port. Math. 12 (1953),
a
1“46.
Sebasti˜o e Silva, J., Le calcul di¬´rentielle et int´gral dans les espaces localement convexes, r´els
a e e e
ou complexes, I, Atti. Acad. Naz. Lincei 20 (1956a), 743“750.
Sebasti˜o e Silva, J., Le calcul di¬´rentielle et int´gral dans les espaces localement convexes, r´els
a e e e
ou complexes, II, Atti. Acad. Naz. Lincei 21 (1956b), 40“46.
Sebasti˜o e Silva, J., Conceitos de fun¸˜ o diferenci´vel em espa¸os localmente convexos, Publ.
a ca a c
do Centro Estudos Math. de Lisboa (1957).
Sebasti˜o e Silva, J., Les espaces ` born´s et la notion de fonction di¬´rentiable, Colloque sur
a a e e
l™analyse fonctionnelle, Louvain, 1960, CBRM, 1961, pp. 57“63.
Seeley, R.T., Extension of C ∞ -functions de¬ned in a half space, Proc. Am. Math. Soc. 15 (1964),
625“626.
Segal, G., The geometry of the KdV equation, Int. J. Mod. Phys. A 6 (1991), 2859“2869.
Seip, U., Kompakt erzeugte Vektorr¨ume und Analysis,, Lecture Notes in Math. 273, Springer-
a
Verlag, Heidelberg, 1972.
Seip, U., Di¬erential calculus and cartesian closedness, Categorical Topology, Mannheim 1975
(Binz, E., Herrlich, H., eds.), Lecture Notes in Math. 540, Springer-Verlag, Heidelberg, 1976,
pp. 578“604.
Seip, U., A convenient setting for di¬erential calculus, J. Pure Appl. Algebra 14 (1979), 73“100.
Seip, U., A convenient setting for smooth manifolds, J. Pure Appl. Algebra 21 (1981), 279“305.
Shirota, A class of topological spaces, Osaka Math. J. 4 (1952), 23“40.
Siegl, E., A free convenient vector space for holomorphic spaces, Monatsh. Math. 119 (1995),
85“97.
Siegl, E., Free convenient vector spaces, doctoral thesis, Universit¨t Wien, Vienna, 1997.
a
Smale, S., Di¬eomorphisms of the 2-sphere, Proc. Am. Math. Soc. 10 (1959), 621“626.
References 609

Sova, M., Conditions of di¬erentiability in topological vector spaces, Czech. Math. J. 16 (1966a),
339“362.
Sova, M., General theory of di¬erentiability in linear topological spaces,, Czech. Math. J. 14
(1966b), 485“508.
Steenrod, N.E., A convenient category for topological spaces, Mich. Math. J. 14 (1967), 133“152.
Stegall, Ch., The Radon-Nikodym property in conjugate Banach spaces, Trans. Am. Math. Soc.
206 (1975), 213“223.
Stegall, Ch., The duality between Asplund spaces and spaces with the Radon-Nikodym property,
Isr. J. Math. 29 (1978), 408“412.
Stegall, Ch., The Radon-Nikodym property in conjugate Banach spaces II, Trans. Am. Math. Soc.
264 (1981), 507“519.
Stein, E.M., Singular integrals and di¬erentiability properties of functions, Princeton Univ. Press,
Princeton, 1970.
Stolz, O., Grundz¨ge der Di¬erential- und Integralrechnung, Bd. 1, Leipzig, 1893.
u
Sullivan, D., In¬nitesimal computations in topology, Publ. Math. Inst. Hautes Etud. Sci. 47
(1978), 269“331.
Sylvester, J., On a theory of the syzygetic relations of two rational integral functions, comprising
an application to the theory of Sturm™s functions, and that of the greatest algebraic common
measure, Philos. Trans. R. Soc. Lond. 143 (1853), 407“548; Mathematical papers, Vol. I, At
the University Press, Cambridge, 1904, pp. 511¬.
Talagrand, M., Renormages de quelques C(K), Isr. J. Math. 54 (1986), 327“334.
Thurston, W., Foliations and groups of di¬eomorphisms, Bull. Am. Math. Soc. 80 (1974), 304“
307.
Toeplitz, O., Die linearen vollkommenen R¨ume der Funktionentheorie, Comment. Math. Helv.
a
23 (1949), 222“242.
Toru´zcyk, H., Smooth partitions of unity on some non“separable Banach spaces, Stud. Math.
n
46 (1973), 43“51.
Toru´czyk, H., Characterizing Hilbert space topology, Fundam. Math. 111 (1981), 247“262.
n
Toru´czyk, H., A correction of two papers concerning Hilbert manifolds, Fundam. Math. 125
n
(1985), 89“93.
Tougeron, J.C., Id´aux de fonctions di¬´rentiables, Ergebnisse 71, Springer-Verlag, Heidelberg,
e e
1972.
Treves, F., Topological vector spaces, distributions, and kernels, Academic Press, New York, 1967.
Trianta¬llou, G., Di¬eomorphisms of manifolds with ¬nite fundamental group, Bull. Am. Math.
Soc. 31 (1994), 50“53.
Troyanski, S.L., Equivalent norms in unseparable B-spaces with an unconditional basis, Teor.
Funkts. Funkts. Anal. Prilozh. 6 (1968), 59“65.
Troyanski, S.L., On locally convex and di¬erentiable norm in certain non-separable Banach spaces,
Stud. Math. 37 (1971), 173“180.
Turner, E., Di¬eomorphisms of a product of spheres, Invent. Math. 8 (1969), 69“82.
Tzafriri, L., Some directions of results in Banach space theory, Functional analysis, surveys and
recent results, North. Holl., 1980, pp. 2“18.
Valdivia, M., Topics in locally convex spaces, North Holland, 1982.
Valdivia, M., Resolution of identity in certain metrizable locally convex spaces, Rev. R. Acad.
Cienc. Exactas Fis. Nat. Madr. 83 (1989), 75“96.
Valdivia, M., Projective resolution of identity in C(K) spaces, Arch. Math. 54 (1990), 493“498.
Vanderwer¬, J., Smooth approximations in Banach spaces, Proc. Am. Math. Soc. 115 (1992),
113“120.
Van Est, W.T. ; Korthagen, T.J., Nonenlargable Lie algebras, Indag. Math. 26 (1964), 15“31.
Van Hove, L., Topologie des espaces fontionnels analytiques et de groupes in¬nis de transforma-
tions, Bull. Cl. Sci., Acad. R. Belg. 38 (1952), 333“351.
Varadarajan, V.S., Harmonic analysis on real reductive groups, Lecture Notes in Mathematics
576, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
Vaˇ´k, L., On one generalization of weakly compactly generated Banach spaces, Stud. Math. 70
sa
(1981), 11“19.
Veblen, O.; Whitehead, J.H.C., The foundations of di¬erential geometry, Cambridge University
Press, Cambridge, 1932.
Ver Eecke, P., Fondements du calcul di¬´rentiel, Presses Universitaires de France, Paris, 1983.
e
610 References

Ver Eecke, P., Applications du calcul di¬´rentiel, Presses Universitaires de France, Paris, 1985.
e
Verde-Star, L., Interpolation and Combinatorial Functions, Stud. Appl. Math. 79 (1988), 65“92.
Vogt, R., Convenient categories of topological spaces for Homotopie theory,, Arch. Math. 22
(1971), 545“555.
Volterra, V., Sopra le funzioni che dipendone de altre funzioni, Nota I,II,III, Rend. Acad. Naz.
Lincei 4 (3) (1887), 97“105, 141“146, 153“158.
´
Waelbroeck, L., Etudes spectrale des alg`bres compl`tes, M´m. Cl. Sci., Collect., Acad. R. Belg.
e e e
31 (1960), 142“.
Waelbroeck, L., Some theorems about bounded structures, J. Funct. Anal. 1 (1967a), 392“408.
Waelbroeck, L., Di¬erentiable Mappings in b-spaces, J. Funct. Anal. 1 (1967b), 409“418.
Warner, F.W., Foundations of di¬erentiable manifolds and Lie groups, Scott Foresman, 1971.
Warner, G., Harmonic analysis on semisimple Lie groups, Volume I, Springer-Verlag, New York,
1972.
Wegenkittl, K., Topologien auf R¨umen di¬erenzierbarer Funktionen, Diplomarbeit (1987), Uni-
a
versit¨t Wien, 1“72.
a
Wegenkittl, K., The space of isometric immersions into Euclidean space, Dissertation (1989),
Universit¨t Wien, 1“147.
a
Weil, A., Th´orie des points proches sur les vari´t´s di¬erentielles, Colloque de topologie et
e ee
g´om´trie di¬´rentielle, Strasbourg, 1953, pp. 111“117.
ee e
Weinstein, A., Symplectic manifolds and their Lagrangian submanifolds, Adv. Math. 6 (1971),
329“345.
Weinstein, A., Lectures on symplectic manifolds, Reg. Conf. Ser. Math. 29 (1977), Am. Math.
Soc..
Wells, J.C., Di¬erentiable functions on Banach spaces with Lipschitz derivatives, J. Di¬er. Geo.
8 (1973), 135“152.
Whitney, H., Analytic extensions of di¬erentiable functions de¬ned in closed sets, Trans. Am.
Math. Soc. 36 (1934), 63“89.
Whitney, H., Di¬erentiable Even Functions, Duke Math. J. 10 (1943), 159“166.
Whitney, H.; Bruhat, F., Quelques propri´t´s fondamentales des ensembles analytiques-r´els,
ee e
Comment. Math. Helv. 33 (1959), 132“160.
Wojty´ ski, W., One parameter subgroups and B-C-H formula, Stud. Math. 111 (1994), 163“185.
n
Yamamuro, S., A theory of di¬erentiation in locally convex spaces, Mem. Am. Math. Soc. 212
(1979).
Yamamuro, S., Notes on the inverse mapping theorem in locally convex spaces, Bull. Austr. Math.
Soc. 21 (1980), 419“461.
Young, W.H., The fundamental theorems of di¬erential calculus, University Press, Cambridge,
1910.
Zhivkov, N.V., Generic Gˆteaux di¬erentiability of directionally di¬erentiable mappings, Rev.
a
Roum. Math. Pure. Appl. 32 (1987), 179“188.
ˇ
Zivkov, N.V., Generic Gˆteaux di¬erentiability of locally Lipschitzian functions, Constructive
a
Function Theory, 1981, So¬a, 1983, pp. 590“594..
Zorn, M.A., Gˆteaux-di¬erentiability and essential boundedness, Duke Math. J. 12 (1945), 579“
a
583.
Index 611

Index

1, 1-norm, 137 “, real analytic, 264
∞ , ∞-norm, 139 “, smooth, 264
„µ0 , ¬rst countable cardinal, 46 “, stereographic, 512
, diagonal mapping, 59 “, vector bundle, 287
augmented local convenient C ∞ -algebra, 316
—β bornological tensor product, 55
β , bornological tensor algebra, 57 automorphism, inner, 373
A<k> , set of points in Ak+1 with pairwise
, bornological symmetric algebra, 57
distinct coordinates, 227
, bornological exterior algebra, 57
1-form, kinematic, 337
B
“, modular, 337
Bµ (x), µ-ball centered at x, 156
“, operational, 337
barrelled locally convex space, 579
1-isolating, 203
base of a vector bundle, 287
A “ space of a ¬ber bundle, 376
basis of a ¬ber bundle, 376
absolutely convex, 576
Bezoutiant matrix, 537
“ convex Lipschitz bound, 17
Bianchi identity, 377
absorbing, 575
biholomorphic mappings, 264
absorbs, 34
bilinear concomitants, natural, 367
addition, local, 441
bipolar U oo , 16
adherence of order ±, Mackey, 49
bornivorous, 34
“, Mackey, 48, 51
“ set, 35
“, sequential, 41
adjoint mapping — , 8 bornological approximation property, 70, 280
“ embedding, 48
“ representation, 373
“ isomorphism, 8
algebra, bounded, 63
“ locally convex space, 575
“, commutative, 57
“ mapping, 19
“, De Rham cohomology, 354
“ tensor product —β , 55
“, exterior, 57
“ vector space, 34
“, formally real commutative, 305
bornologically compact set, 62, 88
“, graded-commutative, 57
“ compact subset, 41
“, symmetric, 57
“ real analytic curve, 99
“, tensor, 57
bornologi¬cation, 35
“, Weil, 306
“ of a locally convex space, 575
algebraic bracket of vector valued di¬erential
forms, 359 bornology of a locally convex space, 8, 575
“ derivation, 358 “ on a set, 21
almost complex structure, 368 bounded set, 575
“ continuous function, 87 “ algebra, 63
alternating tensor, 57 “ completant set, 580
alternator, alt, 57 “ linear mapping, 8
analytic subsets, 241 “ mapping, 19
anti-derivative, 20 “ modules, 63
approximation of unity, 27 bounding set, 19
“ property, bornological, 70, 280 bump function, 153
“ property, Mackey, 70
C
arc-generated vector space, 39
c∞ -approximation property, 70
Asplund space, 135
c∞ -complete space, 20
“ space, weakly, 136
c∞ -completion, 47
associated bundle, 382
c∞ -open set, 19
atlas, 264
c∞ -topology, 19
“, equivalent, 264
C ∞ , smooth, 30
“, holomorphic, 264
C ∞ (R, E), space of smooth curves, 28
“, principal bundle, 380
612 Index

C ∞ (U, F ), space of smooth mappings, 30 complete space, Mackey, 15
∞ “ space, locally, 20
Cb , space of smooth functions with bounded
derivatives, 159 completely regular space, 46
∞ -algebra, augmented local convenient, 316 completion of a locally convex space, 16
C
C ∞ -algebras, Chart description of functors complex di¬erentiable mapping, 81
complexi¬cation MC of manifold M , 20
induced by, 316
∞ -structure, 264 composition, smoothness of, 444
C
C∞ (M, N ), manifold of smooth mappings, 439 “, truncated, 431
C k -topology, compact-open, 436 conjugate pair, dual, 586
C k -topology, Whitney, 436 “ pair, 583
Cb , space of C k -functions with k-th derivative
k conjugation, 373
connection, 366
bounded, 159
k , space of C k -functions with k-th derivative “ form, Lie algebra valued, 387
CB
“ on a ¬ber bundle, 376
bounded by B, 159
ω -manifold structure of C ω (M, N ), 442 “, classifying, 485
C
C ω -manifold structure on C∞ (M, N ), 443 “, induced, 394, 394
“, linear, 396, 397
c0 -ext, a class of locally convex spaces, 212
“, principal, 387
c0 (“), space of 0-sequences, 142
connections, space of, 479
c0 (X), 50
connector, 397
Cc (X), 50
contact di¬eomorphisms, 467
canonical ¬‚ip, 293
“ distribution, 467
“ involution, 293
“ form, 467
carrier of a mapping, 153
“ graph of a di¬eomorphism, 470
Cartan developing, 427
“ manifold, 467
Cartesian closedness, 30
ˇ “ structure, exact, 467
Cech cohomology set, 288
continuous derivation over eva , 276
chain rule, 33
convenient co-algebras, 246
characteristic vector ¬eld, 467
“ C ∞ -algebra, augmented local, 316
chart changing mapping, 264
“ description of functors induced by C ∞ - “ vector space, 2, 7, 20
convex function, dual of a, 131
algebras, 316
convolution, 27
“ description of Weil functors, 307
coproduct, 576
“ of a foliation, distinguished, 273
cotangent bundle, kinematic, 337
“, vector bundle, 287
“ bundle, operational, 337
“, submanifold, 268
CO-topology, 434
Christo¬el forms, 377
covariant derivative, 397
classifying connection, 485
“ exterior derivative, 392, 399
“ space, 485, 487
“ Lie derivative, 399
closed di¬erential forms, 353
covering space, universal, 271
co-algebras, convenient, 246
COk -topology, 436
co-commutative, 246
curvature, 366, 398
cocurvature of a connection, 366
curve, bornologically real analytic, 99
cocycle condition, 288, 376, 414
“, di¬erentiable, 8
“ of transition functions, 288, 376
“, holomorphic, 81

<< . .

. 95
( : 97)



. . >>