Integral equalities for functions of unbounded spectral operators in Banach spaces / Silvestri B. - Warszawa: Institute of mathematics, Polish academy of sciences, 2009. - 60 p. - (Dissertationes mathematicae; 464) - ISSN 0012-3862  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Contents

Introduction .................................................... 5 Summary of the main results .................................... 11 1. Extension theorem. The case of the strong operator topology .................................................... 12 1.1. Key lemma .............................................. 12 1.2. Extension theorem for strong operator integral equalities ............................................. 19 1.3. Generalization of the Newton-Leibniz formula ........... 26 1.4. Application to resolvents of unbounded scalar type spectral operators in a Banach space G ................. 35 2. Extension theorem. The case of the topology σ(B(G),Ν) ....... 38 2.1. Introduction ........................................... 38 2.2. Existence of the weak integral with respect to the σ(B(G),Ν)-topology ..................................... 38 2.3. Commutation and restriction properties ................. 44 2.4. Extension theorem for integral equalities with respect to the σ(B(G),Ν)-topology ...................... 52 2.5. Generalization of the Newton-Leibniz formula ........... 57 References ..................................................... 59