Research
Research
Research
Research
216+ open-access research outputs.
The Nobel Prize in literature 1965 was awarded Mikhail Sholokhov (1905-1984), for the epic novel Tikhij Don about Cossack life and the birth of a new Soviet society (And Quiet Flows the Don, or The Qu…
Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark …
Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P…
This study presents a hybrid topic modelling framework for computational literary analysis that integrates Latent Dirichlet Allocation (LDA) with sparse Partial Least Squares Discriminant Analysis (sP…
We study the solvability and uniqueness for several degenerate Monge--Amp\`ere equations including the Monge--Amp\`ere eigenvalue problem in real Euclidean spaces that involve singular Borel measures.…
We respond to the critique by Aleksandr V. Korolev and Evgeny F. Talantsev on the superconducting phase fraction ($f$) calculations in Li et al. Nature 649, 871-878 (2026). First, the weak upturn in t…
We develop an Aleksandrov reflection framework for a large class of expanding curvature flows in hyperbolic space, with inverse mean curvature flow serving as a model case. The method applies to the l…
In this paper, integral Gauss curvature of pseudo-cones is extended to the Orlicz setting and the corresponding Orlicz-Aleksandrov problem is studied. By the direct variational method and a restrictiv…
We study a class of parabolic equations in non-divergence form with measurable coefficients that exhibit singular and/or degenerate behavior governed by weights in the $A_{1+\frac{1}{n}}$-Muckenhoupt …
Alessandro Fig\`a-Talamanca (1938-2023) was an influential Italian mathematician, scientific leader of the Italian group of harmonic analysis for many years. Since the late 1970ies, his interest focus…
Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a globa…
We solve the commutant lifting and interpolation problems in the setting of the Hardy space and Schur functions on the open unit ball of $\mathbb{C}^n$. Our solutions also signify the role of inner fu…
In this paper, we study a new class of fully nonlinear uniformly elliptic equations with a so-called harmonic map-like structure, whose model case is given by \begin{equation*} \mathcal{M}^{\pm}_{\lam…
We outline the development of the research group of Harmonic Analysis in Italy and the personality of its founder, Alessandro Fig\`a-Talamanca.…
We prove Aleksandrov-Bakelman-Pucci estimates and Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear pseudo-$p$-Laplacian equations in nondivergence form. Our main a…
In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give several characterizati…
In this paper, we study the $L_p$ dual Minkowski problem for all $q, p \in \mathbb{R}$ from an algebraic perspective. We establish the existence of solutions for group-invariant convex bodies (not nec…
This paper proposes an inexact Aleksandrov-solution-based iteration method, formulated by adapting the convergent Rayleigh inverse iterative scheme introduced by Abedin and Kitagawa, to solve real Mon…
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new f…
This paper describes the theory of Minkowski problems for geometric measures in convex geometric analysis. The theory goes back to Minkowski and Aleksandrov and has been developed extensively in recen…
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