Notions of Convexity

@inproceedings{Hrmander1994NotionsOC,
  title={Notions of Convexity},
  author={Lars H{\"o}rmander},
  year={1994}
}
The first two chapters of the book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets and sets which are convex for supports or singular supports with respect to a differential operator. In addition the… 
View via Publisher
link.springer.com
716 Citations
Highly Influential Citations
52
Background Citations
183
Methods Citations
47
Results Citations
3

716 Citations

Order Versions of the Hahn–Banach Theorem and Envelopes. II. Applications to Function Theory

In this paper, we consider the problem on the existence of the upper (lower) envelope of a convex cone or, more generally, a convex set for functions on the projective limit of vector lattices with…

On the solvability of linear partial differential equations in spaces of hyperfunctions

It is well known from the theory of linear partial differential equations in spaces of smooth functions and distributions, see HSrmander [11], [12], that the solvability of a differential equation is…

A new characterization of convexity in free Carnot groups

A characterization of convex functions in RN states that an upper semicontinuous function u is convex if and only if u(Ax) is subharmonic (with respect to the usual Laplace operator) for every…

A characterization of the concept of duality

In this paper we discuss the abstract concept of duality. We consider various classes: convex functions, s-concave functions, convex bodies and log-concave functions. We demonstrate how very little…

On the regularity of solutions of quasilinear Poisson equations

without any assumptions on the sign and zeros of the right-hand side in (1). We analyze how the degree of regularity of solutions depends on the degree of integrability of the multiplier h. On the…

Motions of Julia sets and dynamical stability in several complex variables

In this thesis we study holomorphic dynamical systems depending on parameters. Our main goal is to contribute to the establishment of a theory of stability and bifurcation in several complex…

Convexity in Real Analysis

We treat the classical notion of convexity in the context of hard real analysis. Definitions of the concept are given in terms of defining functions and quadratic forms, and characterizations are…

Some polynomial inequalities on real normed spaces

We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski…

On convexity of level sets of p-harmonic functions

Some Polynomial Inequalities on Real Normed Spaces

We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski…
...