On the domain of the implicit function and applications.
On the notions of absolute continuity for functions of several variables
Absolutely continuous functions of n variables were recently introduced by J. Malý [5]. We introduce a more general definition, suggested by L. Zajíček. This new absolute continuity also implies continuity, weak differentiability with gradient in Lⁿ, differentiability almost everywhere and the area formula. It is shown that our definition does not depend on the shape of balls in the definition.
On the singular support of the distributional determinant
On weak Hessian determinants
We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.
Parametric monotone generalized equations in reflexive Banach spaces.
Polynomials and degrees of maps in real normed algebras
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...
Projectively Solid Sets and an N-dimensional Piccard's Theorem
We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property.
Solution de la question 1570, proposée par M. Rouché
Some Functional Inequalities.
Some inverse mapping theorems
Some versions of limit and Dieudonné-type theorems with respect to filter convergence for (ℓ)-group-valued measures
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
Spectral synthesis and the Pompeiu problem
It is shown that every closed rotation and translation invariant subspace of or , , is of spectral synthesis, i.e. is spanned by the polynomial-exponential functions it contains. It is a classical problem to find those measures of compact support on with the following property: (P) The only function satisfying for all rigid motions of is the zero function. As an application of the above result a characterization of such measures is obtained in terms of their Fourier-Laplace transforms....
Sur les arcs de certaines courbes sphériques
Sur quelques théorèmes fondamentaux de l'algèbre moderne
Sur une propriété des déterminants fonctionnels et son application au développement des fonctions implicites.
Tafeln der eindeutig umkehrbaren Functionen zweier Variabeln auf den einfachsten Zahlengebieten.
The linear topological quasiconformality coefficient and sufficient conditions for the branch points of mappings.
The plenary hull of the generalized Jacobian matrix and the inverse function theorem in subdifferential calculus
The space : minimal connection and optimal lifting
Ueber die Umkehrung der Systeme von Functionen reeller Variabeln