On some classes of q-plurisubharmonic functions and q-pseudoconcave sets / vorgelegt von Thomas Patrick Pawlaschyk. Wuppertal, 2015
Inhalt
- I Introduction
- II Real q-convexity and q-plurisubharmonicity
- Semi-continuity
- Upper semi-continuous functions
- Upper semi-continuous regularization
- Maximal values
- Upper semi-continuity in normed spaces
- Monotone closures
- Real q-convexity
- Convex sets and functions
- Regularity of convex functions
- Real q-convex functions
- Strictly and smooth real q-convex functions
- Twice differentiable real q-convex functions
- Approximation of real q-convex functions
- q-Plurisubharmonicity
- Holomorphic and pluriharmonic functions
- Subpluriharmonic functions
- q-Plurisubharmonic functions
- Smooth and strictly q-plurisubharmonic functions
- Approximation of q-plurisubharmonic functions
- Real q-convex and q-plurisubharmonic functions
- Weakly q-plurisubharmonic functions
- q-Plurisubharmonic functions on analytic sets
- r-Plurisubharmonic functions on foliations
- q-Holomorphic functions
- Holomorphic functions on foliations
- III q-Pseudoconvexity and q-Shilov boundaries
- q-Pseudoconvexity
- q-Pseudoconvex sets
- Boundary distance functions
- Equivalent notions of q-pseudoconvexity
- Real q-convex and q-pseudoconvex sets
- Smoothly bounded q-pseudoconvex sets
- Duality principle of q-pseudoconvex sets
- q-Pseudoconcave graphs
- Generalized convex hulls
- Hulls created by q-plurisubharmonic functions
- More generalized convex q-hulls
- q-Maximal sets and q-hulls
- The Bergman-Shilov boundary
- Shilov boundary for upper semi-continuous functions
- Existence of the Shilov boundary
- Minimal boundary and peak points
- Peak point theorems
- The q-Shilov boundaries
- Shilov boundary and q-plurisubharmonicity
- Shilov boundary and q-holomorphicity
- Lower dimensional q-Shilov boundaries
- Shilov boundary of q-th order
- Real and q-complex points
- q-Shilov boundaries of convex sets
- References
- Index