Książka - szczegóły

CONTENTS

Introduction................................................................................................................................... 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. $D_D_0$ $\varsubsetneqq$ $X_0(Z)$.......................................................................... 32
 3. The D-R homomorphism theorem................................................................................. 33
  3.1. Eigenvectors of D and R................................................................................. 35
 4. The D-R homomorphism theorem for $D_D_0$ $\varsubsetneqq$ X.................. 35
 5. $d_0$-topology................................................................................................................... 38