Related papers: Valuations and plurisubharmonic singularities

This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.

We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We…

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…

The main purpose of this paper is to introduce and study the notion of plurifinely-maximal plurifinely plurisubharmonic functions, which extends the notion of maximal plurisubharmonic functions on a Euclidean domain to a plurifine domain of…

The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…

We study the ring of arithmetical functions with unitary convolution, giving an isomorphism to a generalized power series ring on infinitely many variables, similar to the isomorphism of Cashwell-Everett between the ring of arithmetical…

Three decades ago, Stanley and Brenti initiated the study of the Kazhdan--Lusztig--Stanley (KLS) functions, putting on common ground several polynomials appearing in algebraic combinatorics, discrete geometry, and representation theory. In…

The aim of this article is to study the residual Monge-Amp\`{e}re mass of a plurisubharmonic function with an isolated singularity, provided with the circular symmetry. With the aid of Sasakian geometry, we obtain an estimate on the…

Let $p,p_1,\ldots,p_m$ be positive integers with $p_1\leq p_2\leq\cdots\leq p_m$ and $x\in [-1,1)$, define the so-called Euler type sums ${S_{{p_1}{p_2} \cdots {p_m},p}}\left( x \right)$, which are the infinite sums whose general term is a…

In this work we obtain boundedness on weighted variable Lebesgue spaces of some maximal functions that come from the localized analysis considering a critical radius function. This analysis appears naturally in the context of the…

We establish operator-valued versions of the earlier foundational factorization results for noncommutative polynomials due to Helton (Ann.~Math., 2002) and one of the authors (Linear Alg.~Appl., 2001). Specifically, we show that every…

We prove the reversed Alexandrov-Fenchel inequality for mixed Monge-Amp\`ere masses of plurisubharmonic functions, which generalizes a result of Demailly and Pham. As applications to convex geometry, this gives a complex analytic proof of…

The convolution properties are discussed for the complex-valued harmonic functions in the unit disk $\mathbb{D}$ constructed from the harmonic shearing of the analytic function $\phi(z):=\int_0^z…

In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\i}ymaz O. A certain generalized Pochhammer symbol and its…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

We consider rational functions of the form $V(x)/U(x)$, where both $V(x)$ and $U(x)$ are polynomials over the finite field $\mathbb{F}_q$. Polynomials that permute the elements of a field, called {\it permutation polynomials ($PPs$)}, have…

Concentration properties of functionals of general Poisson processes are studied. Using a modified $\Phi$-Sobolev inequality a recursion scheme for moments is established, which is of independent interest. This is applied to derive moment…

Let $E$ and $F$ be complex Banach spaces, $U$ be an open subset of $E$ and $1\leq p\leq\infty$. We introduce and study the notion of a Cohen strongly $p$-summing holomorphic mapping from $U$ to $F$, a holomorphic version of a strongly…

A notion of local indicator for a plurisubharmonic function is introduced. The indicator is a certain plurisubharmonic function in the unit polydisc, which controls the behavior of the considered function near a fixed point of its…

Many aspects of pluripotential theory are generalized to quaternionic $m$-subharmonic functions. We introduce quaternionic version of notions of the $m$-Hessian operator, $m$-subharmonic functions, $m$-Hessian measure, $m$-capapcity, the…