A class of globally univalent differentiable mappings
A counterexample to the strong real Jocobian conjecture.
A historical outline of the theorem of implicit functions.
A Jacobian condition for injectivity of differentiable plane maps
A note on global implicit function theorem.
A proof of the inverse function theorem
An implicit-function theorem for a class of monotone generalized equations
Approximations and error bounds for computing the inverse mapping
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
Beiträge zur der Theorie der Umkehrung eines Functionensystems.
Bemerkungen zu Determinanten-Theorie. Auszug aus Briefen an Herrn Baltzer.
Change of variables formula under minimal assumptions
In the previous papers concerning the change of variables formula (in the form involving the Banach indicatrix) various assumptions were made about the corresponding transformation (see e.g. [BI], [GR], [F], [RR]). The full treatment of the case of continuous transformation is given in [RR]. In [BI] the transformation was assumed to be continuous, a.e. differentiable and with locally integrable Jacobian. In this paper we show that none of these assumptions is necessary (Theorem 2). We only need...
Conditions pour que les constantes arbitraires d'une expression générale soient distinctes entre elles.
Convolution operators with homogeneous singular measures on of polynomial type. The remainder case.
Définition axiomatique de la mesure de Hausdorff
Diferenciální počet II [Book]
Differential conditions to verify the Jacobian Conjecture
Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Ein Satz über eindeutige Abbildung und seine Anwendung in der Variationsrechnung
Eine Funktionalgleichung für operatorwertige Funktionen.
Elliptic complexes in the calculus of variations [Book]
Extremal tests for scalar functions of several real variables at degenerate critical points.