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On some classes of q-plurisubharmonic functions and q-pseudoconcave sets / vorgelegt von Thomas Patrick Pawlaschyk. Wuppertal, 2015
Content
I Introduction
Historical overview
Chapter overview and new results
Basic notations
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