相关论文: Log-biharmonicity and a Jensen formula in the spac…
We develop and use some key concepts of potential theory, such as balayage and duality between measures and their potentials, to study the distribution of masses of subharmonic functions while restrictions to their growth near the boundary…
A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured…
We prove a Jensen formula for slice-regular functions of one quaternionic variable. The formula relates the value of the function and of its first two derivatives at a point with its integral mean on a three dimensional sphere centred at…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
On even-dimensional Euclidean space for integer powers of the Laplace operator greater than or equal to half the dimension, a fundamental solution of the polyharmonic equation has binomial and logarithmic behavior. Gegenbauer polynomial…
It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of closed faces of a compact convex set which has been thoroughly…
We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in \cite{Ji2}, \cite{CH}, \cite{CMO1},…
We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is…
We estimate the energy and Hausdorff dimensions of the Riesz products on the unit sphere of $\mathbb{C}^n$, $n\ge 2$. Also, we obtain similar results for the pluriharmonic measures on the torus.
We extend the notion of quasibounded harmonic functions to the plurisubharmonic setting. As an application, using the theory of Jensen measures, we show that certain generalized Dirichlet problems with unbounded boundary data admit unique…
We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…
In this note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier \cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it is expected that…
Nevanlinna theory studies the value distribution of meromorphic functions and provides powerful results in the form of the First and Second Main Theorems. In this paper, we introduce quaternionic analogues of the Nevanlinna functions.…
The transference theory for Lp spaces of Calderon, Coifman, and Weiss is a powerful tool with many applications to singular integrals, ergodic theory, and spectral theory of operators. Transference methods afford a unified approach to many…
We introduce a measure of coherence, which is extended from the coherence rank via the standard convex roof construction, we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory,…
This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
For a general set transformation ${\cal R}$ between two measure spaces, we define the rearrangement of a measurable function by means of the Layer's cake formula. We study some functional properties of the Lorentz spaces defined in terms of…
We extend the trace-logarithmic $S$-divergence from matrices to tracial $C^*$-algebras and finite von Neumann algebras, and show that its square root defines a metric on the invertible positive cone. We also prove an integral representation…
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensional Hilbert space. On the set of all Gaussian measures…