Related papers: The third Cauchy-Fantappie formula of Leray
In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei. First, the existence, the positivity and the long time behavior of…
It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A…
We show existence of unique smooth solutions to the Monge-Ampere equation for (n-1)-plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As a consequence we obtain Calabi-Yau theorems for Gauduchon…
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus, O.G. Smolyanov concerning the existence of a strongly continuous operator semigroup solving a Cauchy-Dirichlet problem for an elliptic differential operator in a…
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the…
In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posedness of fractional-type anomalous unidirectional diffusion…
In this paper, we obtain conditions of Noetherian solvability and the Index formula for a singular integral equation with a Cauchy kernel and a Carleman shift in Besov space, which is embedded into the space of continuous functions on a…
We show how Cauchy's Integral Formula and the ideas of Dunford's Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables…
The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensional linear space is extended to conditional expectations and…
Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and…
We study the discrete cohomological equation of a hyperbolic affine automorphism Y of the torus (whose linear part is not necessarily diagonalisable). More precisely ; if d is the cobord operator defined by : d (h) = h-hoY for every element…
We utilise a quotient of the universal enveloping algebra of the Poincar\'e algebra in three spacetime dimensions, on which we formulate a covariant constancy condition. The equations so obtained contain the Fierz-Pauli equations for…
By using Cauchy integral formula in the theory of complex functions, the authors establish some integral representations for the principal branches of several complex functions involving the logarithmic function, find some properties, such…
Let $\ID$ denote the open unit disc and let $p\in (0,1)$. We consider the family $Co(p)$ of functions $f:\ID\to \overline{\IC}$ that satisfy the following conditions: \bee \item[(i)] $f$ is meromorphic in $\ID$ and has a simple pole at the…
We consider the Cauchy problem for a second-order nonlinear evolution equation in a Hilbert space. This equation represents the abstract generalization of the Ball integro-differential equation. The general nonlinear case with respect to…
We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…
Krasnov (arXiv: hep-th/0005106) identified the renormalized volume of a Schottky 3-manifold with the action of the Liouville theory on the conformal infiinity. We try to compute the renormalized volume in terms of more transparent geometric…
We derive integral representations for $(0,q)$-forms, $q\ge1$, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains. A $(0,q)$-form, $f$ is written in terms of integral operators acting on $f$, $\mdbar f$, and…
In this note, we prove in full generality a conjecture of Jacquet concerning the nonvanishing of the triple product L-function at the central point. Let $\kay$ be a number field and let $\pi_i$, $i=1$, 2, 3 be cuspidal automorphic…
Chapter 1 deals with the problem of the existence of an upper/lower envelope from a convex cone or, more generally, a convex set for functions on the projective limit of vector lattices with values in the completion of the Kantorovich space…