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Differentiable structure in a conjugate vector bundle of infinite dimension

Seria
Rozprawy Matematyczne tom/nr w serii: 113 wydano: 1974
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CONTENTS
Introduction
Chapter I. Differentiation in Cartesian products of normed and infrabarrelled of DF-type spaces
§ 1. Preliminaries......................................................................................................................................................................... 7
§ 2. Fundamental definitions...................................................................................................................................................... 7
§ 3. Certain properties of mappings in some l.e.v-.v. space................................................................................................ 9
§ 4. Mean value theorems .......................................................................................................................................................... 11
§ 5. Differentiation of a superposition....................................................................................................................................... 14
§ 6. Higher order derivatives....................................................................................................................................................... 15
Chapter II. Differential calculus in Marinescu spaces
§ 1. Basic concepts and definitions.......................................................................................................................................... 16
§ 2. Differentiation in Marinescu spaces.................................................................................................................................. 17
§ 3. Differential calculus in bornological Von-Neumann spaces........................................................................................ 21
Chapter III. Differentiable structure in a conjugate bundle
§ 1. Non-banachian differentiable manifolds.......................................................................................................................... 24
§ 2. Infinite-dimensional vector bundles.................................................................................................................................. 25
§ 3. Conjugate bundle......................................................................................................................................................................... 26
Chapter IV. The bundle of section-distributions
§ 1. The bundle of section-distributions................................................................................................................................... 29
§ 2. An application in the field theory......................................................................................................................................... 31
§ 3. Example of a Lagrangian.................................................................................................................................................... 32
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 113
Liczba stron
33
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXIII
Daty
wydano
1974
Twórcy
Bibliografia
  • [1] B. H. Arnold, Topologies defined by hounded sets, Duke Math. J. 18 (1951), pp. 631-642.
  • [2] A. Bastiani, Applications différëntiables et variétés différentiables de dimension infinie, J. Anal. Math. 13 (1964), pp. 1-114.
  • [3] N. Bourbaki, Fonctions d'une variable réelle, Paris 1958.
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  • [5] J. Dieudonné, Foundations of modem analysis, New York 1960.
  • [6] E. Dubinsky, Differential calculus in Montel spaces, Trans. Amer. Math. Soc. 110 (1964), pp. 1-24.
  • [7] H. R. Fischer, Limesräume, Math. Ann. 137 (1959), pp. 269-303.
  • [8] A. Frölicher and W. Bucher, Calculus in vector spaces without norm, Lecture Notes in Math. 30 (1966).
  • [9] A. Grothendieck, Sur les espaces (F) et (DF), Summa Bras. Math. 3 (1954), pp. 57-123.
  • [10] H. Hogbe-Nlend, Théorie des Bornologies et Applications, Lecture Notes in Math. 213 (1971).
  • [11] H. Jarchow, Marinescu Räume, Comm., Math. Helv. 44 (1969), pp. 138-163.
  • [12] H. Keller, Differenzierbarkeit in topologischen Vectorräumen, Comm, Math. Helv. 38 (1964), pp. 308-320.
  • [13] J. Kijowski and J. Komorowski, A differentiable structure in the set of all bundle sections over compact subsets, Studia Math. 32 (1969), pp. 191-207.
  • [14] J. Kijowski, Existence of differentiable structure in the set of submanifolds, Studia Math. 33 (1969), pp. 93-108.
  • [15] J. Kijowski and W. Szczyrba, On differentiability in an important class of locally convex spaces, Studia Math. 30 (1968), pp 247-257.
  • [16] J. Kisyński, Convergence du type L, Coll. Math. 72(1960), pp. 205-211.
  • [17] J. Komorowski, A geometrical formulation of the general free boundary problems, Reports Math. Phys. 1 (1970), pp. 105-133.
  • [18] S. Lang, Introduction to differentiable manifold, New York 1962.
  • [19] B. Malgrange, Ideals of differentiable functions, Oxford 1966.
  • [20] G. Marinescu, Différentielles de Gâteaux et Fréchet dans les espaces localement convexes. Bull. Math. Soc. Sci. Math.-Phys. R.P.R. 1 (1957), pp. 77-86.
  • [21] G. Marinescu, Espaces vectoriels pseudotopologiques et théorie des distributions, Berlin 1963.
  • [22] J. Mikusiński, Distributions à valeurs dans les réunions d'espaces de Banach, Studia Math. 29 (1960), pp. 249-285.
  • [23] J. Rzewuski, Field Theory I, Warszawa 1958.
  • [24] L. Schwartz, Théorie des distributions, Paris 1966.
  • [25] J. Sebastião e Silva, Les espaces à bornes et la notion de fonction différentiable, Atti Acc. Naz. dei Lincei, Serie VIII, 34 (1963), pp. 57-61.
  • [26] J. Sebastião e Silva, Les espaces à bornes et les reunions d'espaces normes, ibidem, pp. 134-137.
  • [27] М. Ф. Сухинин, О локальной обратимости дифференцируемого отображения, У.М.Н. 15, 5 (1970), pp. 249-250.
  • [28] W. Szczyrba, Differentiation in locally convex spaces, Studia Math. 39 (1971), pp. 289-306.
  • [29] P. Urbański, Dissertation- for the Ph. D. degree.
  • [30] L. Waelbrock, Les espaces à bornes complètes, Colleque but l'Analyse Fonctionelle CBRM 1961, pp. 51-57.
  • [31] K. Wilmański, Dynamics of bodies with microstructure, Archiwum Mechaniki Stosowanej 6, 20 (1968), pp. 705-743.
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