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Differentiable structure in a conjugate vector bundle of infinite dimension

100%

Urbański P.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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An affine framework for analytical mechanics

96%

Urbański P.

Banach Center Publications

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2003

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tom 59

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nr 1

257-279

EN

An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine setting are proved.

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STANISŁAW ZAKRZEWSKI (28.6.1951-30.4.1998)

37%

Kijowski J., Urbański P., Woronowicz S. L.

Banach Center Publications

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2000

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tom 51

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nr 1

9-10

Ograniczanie wyników

2 Banach Center Publications

3 Urbański P.

1 Kijowski J.

1 Woronowicz S. L.

1 2003

1 2000

1 1974

Differentiable structure in a conjugate vector bundle of infinite dimension

An affine framework for analytical mechanics

STANISŁAW ZAKRZEWSKI (28.6.1951-30.4.1998)