Non-Homogeneous Boundary Value Problems and Applications

7 Scalar and Vector Ultra-Distributions.- 1. Scalar-Valued Functions of Class Mk.- 2. Scalar-Valued Ultra-Distributions of Class Mk; Generalizations.- 3. Spaces of Analytic Functions and of Analytic Functionals.- 4. Vector-Valued Functions of Class Mk.- 5. Vector-Valued Ultra-Distributions of Class Mk; Generalizations.- 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.- 2. The Theorem on "Elliptic Iterates": Proof.- 3. Application of Transposition; Existence of Solutions in the Space D'(?) of Distributions.- 4. Existence of Solutions in the Space $$D{'_{{M_k}}}\left( \Omega \right)$$ of Ultra-Distributions.- 5. Comments.- 6. Problems.- 9 Evolution Equations in Spaces of Distributions and Ultra-Distributions.- 1. Regularity Results. Equations of the First Order in t.- 2. Equations of the Second Order in t.- 3. Singular Equations of the Second Order in t.- 4. Schroedinger-Type Equations.- 5. Stability Results in Mk-Classes.- 6. Transposition.- 7. Semi-Groups.- 8. Mk -Classes and Laplace Transformation.- 9. General Operator Equations.- 10. The Case of a Finite Interval ]0, T[.- 11. Distribution and Ultra-Distribution Semi-Groups.- 12. A General Local Existence Result.- 13. Comments.- 14. Problems.- 10 Parabolic Boundary Value Problems in Spaces of Ultra-Distributions.- 1. Regularity in the Interior of Solutions of Parabolic Equations.- 2. The Regularity at the Boundary of Solutions of Parabolic Boundary Value Problems.- 3. Application of Transposition: The Finite Cylinder Case.- 4. Application of Transposition: The Infinite Cylinder Case.- 5. Comments.- 6.Problems.- 11 Evolution Equations of the Second Order in t and of Schroedinger Type.- 1. Equations of the Second Order in t; Regularity of the Solutions of Boundary Value Problems.- 2. Equations of the Second Order in t; Application of Transposition and Existence of Solutions in Spaces of Distributions.- 3. Equations of the Second Order in t; Application of Transposition and Existence of Solutions in Spaces of Ultra-Distributions.- 4. Schroedinger Equations; Complements for Parabolic Equations.- 5. Comments.- 6. Problems.- Appendix. Calculus of Variations in Gevrey-Type Spaces.