Analyse fonctionnelle : une introduction pour physiciens by N. Boccara. PDF

By N. Boccara.

ISBN-10: 2729896058

ISBN-13: 9782729896058

Dans ce chapitre sont construits les outils indispensables a l'élaboration des théories qui seront développées par los angeles suite. los angeles suggestion de mesure у joue un rôle essentiel. Les résultats les plus importants sont le théorème de los angeles convergence dominée de Lebesgue et le théorème de Fubini relatif a l'interversion des ordres d’intégration dans les intégrales multiples.
Plus encore dans ce chapitre que dans les suivants, il est recommande de se familiariser avec ces théorèmes, en étudiant les différents exemples et en essayant de faire les exercices, avant d'en aborder l. a. démonstration.

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Example text

L. DE BRANGES DE BOURCIA March 4, 2004 31 Theorem 8. If D(U ) is the state space of a canonical unitary linear system with transfer function U (z) and if D(V ) is the state space of a canonical unitary linear system with transfer function V (z) such that the inequality 1 ≤ [1 − |U (z)|2 ]−1 + [1 − |V (z)|2 ]−1 holds when z is in the unit disk, then a Hilbert space E exists whose elements are the pairs (u(z), v(z)) of power series u(z) = f (z) + U (z)h(z) and v(z) = k(z) + V ∗ (z)g(z) for elements (f (z), g(z)) of the space D(U ) and (h(z), k(z)) of the space D(V ) and which satisfies the identity (u(z), v(z)), (u(z), v(z)) sD(W ) = (f (z), g(z)), (f (z), g(z)) D(U) + (h(z), k(z)), (h(z), k(z)) D(V ) .

L. de Branges, Factorization and invariant subspaces, Journal of Mathematical Analysis and Applications 19 (1970), 163–200. 3. , Complementation in Krein spaces, Transactions of the American Mathematical Society 305 (1988), 277–291. 4. , Krein spaces of analytic functions, Journal of Functional Analysis 81 (1988), 219–259. 5. , A proof of the Bieberbach conjecture, Acta Mathematica 154 (1985), 137–150. 6. , Powers of Riemann mapping functions, The Bieberbach Conjecture, Proceedings of the Symposium on the Occasion of the Proof, Mathematical Surveys, Volume 21, American Mathematical Society, Providence, 1986, 51-67.

Powers of Riemann mapping functions, The Bieberbach Conjecture, Proceedings of the Symposium on the Occasion of the Proof, Mathematical Surveys, Volume 21, American Mathematical Society, Providence, 1986, 51-67. 7. , Unitary linear systems whose transfer functions are Riemann mapping functions, Operator Theory: Advances and Applications 19 (1986), Birkh¨ auser Verlag, Basel, 105–125. 8. L. de Branges and J. Rovnyak, Square Summable Power Series, Holt, Rinehart, and Winston, New York, 1966. 32 9.

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Analyse fonctionnelle : une introduction pour physiciens by N. Boccara.


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