CONTENTSIntroductionChapter 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....................................................................................................................................................... 15Chapter 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........................................................................................ 21Chapter III. Differentiable structure in a conjugate bundle§ 1. Non-banachian differentiable manifolds.......................................................................................................................... 24§ 2. Infinite-dimensional vector bundles.................................................................................................................................. 25§ 3. Conjugate bundle......................................................................................................................................................................... 26Chapter 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
@book{bwmeta1.element.zamlynska-aa24e776-ae50-4b68-9cf7-46012a781387,
author = {Pawe\l\ Urba\'nski},
title = {Differentiable structure in a conjugate vector bundle of infinite dimension},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1974},
zbl = {0298.58003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-aa24e776-ae50-4b68-9cf7-46012a781387}
}
Paweł Urbański. Differentiable structure in a conjugate vector bundle of infinite dimension. GDML_Books (1974), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-aa24e776-ae50-4b68-9cf7-46012a781387/