相关论文: Generalized Jacobian for Functions with Infinite D…

In dimension 2, we introduce a distributional Jacobian determinant $\det DV_\beta(Dv)$ for the nonlinear complex gradient $(x_1,x_2)\mapsto |Dv|^\beta(v_{x_1},-v_{x_2})$ for any $\beta>-1$, whenever $v\in W^{1,2 }_{\text{loc}}$ and $\beta…

When $k$ is a field, the classical Jacobian criterion computes the singular locus of an equidimensional, finitely generated $k$-algebra as the closed subset of an ideal generated by appropriate minors of the so-called Jacobian matrix.…

This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value…

We clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho, and the GFDA spaces introduced in our earlier paper on differentiability of Lipschitz maps into Banach spaces.

We revisit the problem of characterizing the eigenvalue distribution of the Dirichlet-Laplacian on bounded open sets $\Omega\subset\mathbb{R}$ with fractal boundaries. It is well-known from the results of Lapidus and Pomerance \cite{LapPo1}…

For finite Galois extension fields defined by odd degree irreducible polynomials over algebraic integer ring, we observe "Reciprocity Law" through Jacobian Variety by embedding all roots of the polynomials into 2-torsion points of Jacobian…

In this work we consider infinite dimensional extensions of some finite dimensional Gaussian geometric functionals called the Gaussian Minkowski functionals. These functionals appear as coefficients in the probability content of a tube…

This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of "regularizer", "barrier", "penalty…

It is established a series of criteria for continuous and homeomorphic extension to the boundary of the so-called lower $Q$-homeomorphisms $f$ between domains in $\overline{\Rn}=\Rn\cup\{\infty\}$, $n\geqslant2$, under integral constraints…

We introduce a real vector space composed of set-valued maps on an open set X and note it by S. It is a complete metric space and a complete lattice. The set of continuous functions on X is dense in S as in a metric space and as in a…

Two generalizations of the Minkowski ?(x) function are given. As ?(x) maps quadratic irrationals to rational numbers, it is shown that both generalizations send natural classes of pairs of cubic irrational numbers in the same cubic number…

We study the Jacobian conjecture for Keller maps $f:X_0:=\mathbf{A}^n\rightarrow Y_0:=\mathbf{A}^n$ in characteristic $0$ and attempt to prove it. We are quite aware of the fact that many people have tried to prove the Jacobian conjecture…

This paper has two main goals. First, we are concerned with the classification of self-adjoint extensions of the Laplacian $-\Delta\big|_{C^\infty_0(\Omega)}$ in $L^2(\Omega; d^n x)$. Here, the domain $\Omega$ belongs to a subclass of…

A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given and…

The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required…

We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally…

In this paper, we extend the characterization of John disks obtained by N\"akki and V\"ais\"al\"a [Exp. Math. 1991] to generalized John domains in higher dimensions under mild assumptions. The main ingredient in this characterization is to…

We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

In this paper we review and derive hyperbolic and trigonometric double summation addition theorems for Jacobi functions of the first and second kind. In connection with these addition theorems, we perform a full analysis of the relation…