Structure properties of D-R spaces

Hartmut von Trotha

GDML_Books, (1981), p.

Résumé

CONTENTSIntroduction................................................................................................................................... 5 Notations.......................................................................................................................... 5§ 1. Preliminaries........................................................................................................................ 6 1. Right invertible operators.................................................................................................. 6 2. D-R vector spaces.............................................................................................................. 7 3. Basic types of D-R spaces............................................................................................... 7  3.1. Examples............................................................................................................. 7 4. Subspaces.......................................................................................................................... 8 5. Homomorphisms............................................................................................................... 8  5.1 Quotient spaces and homomorphisms......................................................... 10§2. The general Taylor theorem............................................................................................... 11 1. The elementary Taylor theorem....................................................................................... 11  1.1. Bands of subspaces....................................................................................... 12 2. The general Taylor theorem............................................................................................. 14§ 3. Structure elements of D-R spaces................................................................................... 17 1. The simple Taylor formula................................................................................................ 17 2. Distinguished subspaces and subspace chains....................................................... 18  2.1. Canonical subspaces of a D-R space........................................................ 18  2.2. The space $D_i$............................................................................................. 19  2.3. The space S...................................................................................................... 19  2.4. The space Q..................................................................................................... 20 3. Extension of the domain of D........................................................................................... 21 4. The structure chain............................................................................................................ 22 5. Components and formal component series................................................................ 23 6. Examples............................................................................................................................. 25§ 4. The D-R homomorphism theorem.................................................................................. 27 1. The D-R reference space $X_0$..................................................................................... 27  1.1. X(Z) as a $D_0-R_0$ space with $D_D_0$ = X(Z)................................... 28  1.2. The $d_0$-convergence................................................................................ 28  1.3. The Volterra property of $X_0$ and eigenspaces of $D_0$...................... 31 2. $D_D_0$ $\UnimplementedOperator $ $X_0(Z)$.......................................................................... 32 3. The D-R homomorphism theorem................................................................................. 33  3.1. Eigenvectors of D and R................................................................................. 35 4. The D-R homomorphism theorem for $D_D_0$ $\UnimplementedOperator $ X.................. 35 5. $d_0$-topology................................................................................................................... 38

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EUDML-ID : urn:eudml:doc:268475