variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima...

theory of functions of several complex variables, a pseudoconvex set is a special type of open set in the n-dimensional complex space Cn. Pseudoconvex sets...

quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense...

inequality Logarithmically convex function Pseudoconvex function Quasiconvex function Subderivative of a convex function "Lecture Notes 2" (PDF). www.stat...

E-invex functions were introduced by Abdulaleem as a generalization of differentiable convex functions. Convex function Pseudoconvex function Quasiconvex...

subharmonic function looks like a kind of convex function, so it was named by Levi as a pseudoconvex domain (Hartogs's pseudoconvexity). Pseudoconvex domain...

constant. In several complex variables, plurisubharmonic functions are used to describe pseudoconvex domains, domains of holomorphy and Stein manifolds. The...

leads to the notion of pseudoconvexity. Cauchy–Riemann equations Holomorphic function Paley–Wiener theorem Quasi-analytic function Infinite compositions...

method Convex analysis — function f such that f(tx + (1 − t)y) ≥ tf(x) + (1 − t)f(y) for t ∈ [0,1] Pseudoconvex function — function f such that ∇f · (y −...

strongly pseudoconvex manifold. The latter means that it has a strongly pseudoconvex (or plurisubharmonic) exhaustive function, i.e. a smooth real function ψ...

problem. Behnke–Stein theorem Levi pseudoconvex solution of the Levi problem Stein manifold Steven G. Krantz. Function Theory of Several Complex Variables...

study smooth but not holomorphic functions, see for example Levi pseudoconvexity. When dealing with holomorphic functions, we could consider the Hessian...

show a pseudoconvex set is a domain of holomorphy. line integral Line integral. Liouville Liouville's theorem says a bounded entire function is a constant...

and only if it is (strictly) pseudoconvex as a CR manifold from the side of the domain. (See plurisubharmonic functions and Stein manifold.) An abstract...

and the plurisubharmonic functions. Geometrically, these classes of functions correspond to convex domains and pseudoconvex domains, but there are also...

converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum...

\Omega } . The decomposition in the theorem is feasible also on many non-pseudoconvex domains. The proof of the theorem follows from Hefer's lemma. Let Ω ⊂...

Epstein, R B Melrose, G A Mendoza, Resolvent of the Laplacian on strictly pseudoconvex domains. Acta Mathematica 167 (1991), no. 1–2, 1–106. C L Epstein, The...

"Sobolev estimates for the complex Green operator on a class of weakly pseudoconvex boundaries". Communications in Partial Differential Equations. 16 (10):...

theorem Holomorphically convex hull Integrally-convex set John ellipsoid Pseudoconvexity Radon's theorem Shapley–Folkman lemma Symmetric set Morris, Carla C...

study of the asymptotics of the Bergman kernel off the boundaries of pseudoconvex domains in C n {\displaystyle \mathbb {C} ^{n}} . He has studied mathematical...

Diederich K, Fornaess JE (1975). "Exhaustion functions and Stein neighborhoods for smooth pseudoconvex domains". Proc Natl Acad Sci U S A. 72 (9): 3279–3280...

Kohn, following earlier work by Kohn, studied the ∂-Neumann problem on pseudoconvex domains, and demonstrated the relation of the regularity theory to the...

a special case. In the theory of functions of several complex variables he introduced the concept of pseudoconvexity during his investigations on the...

property than quasiconvexity. A linear-fractional objective function is both pseudoconvex and pseudoconcave, hence pseudolinear. Since an LFP can be transformed...

her Ph.D. in 1993. Her doctoral dissertation, Hardy Spaces on Strongly Pseudoconvex Domains in C n {\displaystyle C^{n}} and Domains of Finite Type in C...

the ∂ ¯ {\displaystyle {\overline {\partial }}} -Neumann problem in pseudoconvex domains of finite type in C {\displaystyle \mathbb {C} } 2 ". Acta Mathematica...

1990 he was an Invited Speaker with talk Some recent results on weakly pseudoconvex domains at the ICM in Kyōto. He was a senior member of the Institut Universitaire...

(1976). "Monge–Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains". Annals of Mathematics. Second Series. 103 (2): 395–416. doi:10...

under Joseph Kohn with thesis Boundary Behavior of Holomorphic Functions on Weakly Pseudoconvex Domains. He is a professor at Purdue University. He solved...