相关论文: Quaternionic plurisubharmonic functions and their …
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…
We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…
We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of…
We show that, in toric manifolds, one can characterize the sign of the Ricci curvature in terms of the convexity of the volume functional. More generally we discuss relationships between (i) Ricci curvature and volume, (ii) totally real and…
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal…
A brief introduction to geometric valuation theory is given. The focus is on classification results for valuations on convex bodies and on function spaces.
In our previous paper, Real Polynomials with a Complex Twist [see http://archives.math.utk.edu/ICTCM/VOL28/A040/paper.pdf], we used advancements in computer graphics that allow us to easily illustrate more complete graphs of polynomial…
In this paper, we introduce the quaternionic slice polyanalytic functions and we prove some of their properties. Then, we apply the obtained results to begin the study of the quaternionic Fock and Bergman spaces in this new setting. In…
We study properties of relative types of plurisubharmonic functions with respect to maximal plurisubharmonic weights. It is shown that they give a general form for upper semicontinuous, tropically additive functionals on plurisubharmonic…
Some results on singularities of plurisubharmonic functions are put into the context of tropical mathematics.
The author introduce the concept of harmonically convex functions and establish some Hermite-Hadamard type inequalities of these classes of functions
We develop the theory of hyperelliptic Kleinian functions. As applications we consider construction of the explicit matrix realization of the hyperelliptic Kummer varieties, differential operators to have the hyperelliptic curve as spectral…
Very recently J. Kotrbaty has proven general inequalities for translation invariant smooth valuations formally analogous to the Hodge- Riemann bilinear relations in the Kahler geometry. The goal of this note is to apply Kotrbaty's theorem…
Convex optimization methods have been extensively used in the fields of communications and signal processing. However, the theory of quaternion optimization is currently not as fully developed and systematic as that of complex and real…
Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic…
This article serves as an introduction to several recent developments in the study of quasisymmetric functions. The focus of this survey is on connections between quasisymmetric functions and the combinatorial Hopf algebra of noncommutative…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…
In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadratic functions are presented. In particular, conditions…