Non-Homogeneous Boundary Value Problems and Applications: Volume III [Paperback]

7 Scalar and Vector Ultra-Distributions.- 1. Scalar-Valued Functions of Class Mk.- 1.1 The Sequences {Mk}.- 1.2 The Space $${D_}\left( H \right)$$.- 1.3 The Spaces $${D_}\left( H \right)$$ and $${\varepsilon _}\left( H \right)$$.- 2. Scalar-Valued Ultra-Distributions of Class Mk; Generalizations.- 2.1 The Space $$D{'_}\left( \Omega \right)$$.- 2.2 Non-Symmetric Spaces of Class Mk.- 2.3 Scalar Ultra-Distributions of Beurling-Type.- 3. Spaces of Analytic Functions and of Analytic Functionals.- 3.1 The Spaces H(H) and H(H).- 3.2 The Spaces H(?) and H(?).- 4. Vector-Valued Functions of Class Mk.- 4.1 The Space $${D_}\left( {\phi ;F} \right)$$.- 4.2 The Spaces $${D_}\left( {H,F} \right)$$ and $${E_}\left( {\phi ;F} \right)$$.- 4.3 The Spaces $${D_{ \pm ,{M_k}}}\left( {\phi ;F} \right)$$.- 4.4 Remarks on the Topological Properties of the Spaces $${D_}\left( {\phi ;F} \right),{E_}\left( {\phi ;F} \right),{D_{ \pm ,{M_k}}}\left( {\phi ;F} \right)$$.- 5. Vector-Valued Ultra-Distributions of Class Mk; Generalizations.- 5.1 Recapitulation on Vector-Valued Distributions.- 5.2 The Space $$D{'_}\left( {\phi ;F} \right)$$.- 5.3 The Space $$D{'_{ \pm ,{M_k}}}\left( {\phi ;F} \right)$$.- 5.4 Vector-Valued Ultra-Distributions of Beurling-Type.- 5.5 The Particular Case: F = Banach Space.- 6. Comments.- 8 Elliptic Boundary Value Problems in Spaces of Distributions and Ultra-Distributions.- 1. Regularity of Solutions of Elliptic Boundary Value Problems in Spaces of Analytic Functions and of Class Mk; Statement of the Problems and Results.- 1.1 Recapitulation on Elliptic Boundary Value Problems.- 1.2 Statement of the Mk-Regularity Results.- 1.3 Reduction of the Problem to the Case of the Half-Ball.- 2. The Theorem on Elliptic Iterates: Proof.- 2.1 Some Lemmas.- 2.2 The Preliminary Estimate.- 2.3 Bounds for the Tangential Derivatives.- 2.4 Bounds for the Normal Derivatives.- 2.5 Proof of Theorem 1.3.- 2.6 Complementlã*