Decomposition of smooth functions of two multidimensional variables
Decompositions of compact convex sets.
Dedekind cuts in C(X)
The aim of this paper is to show that every Hausdorff continuous interval-valued function on a completely regular topological space X corresponds to a Dedekind cut in C(X) and conversely.
Defects and transformations of quasi-copulas
Six different functions measuring the defect of a quasi-copula, i. e., how far away it is from a copula, are discussed. This is done by means of extremal non-positive volumes of specific rectangles (in a way that a zero defect characterizes copulas). Based on these defect functions, six transformations of quasi-copulas are investigated which give rise to six different partitions of the set of all quasi-copulas. For each of these partitions, each equivalence class contains exactly one copula being...
Defining complete and observable chaos
For a continuous map f from a real compact interval I into itself, we consider the set C(f) of points (x,y) ∈ I² for which and . We prove that if C(f) has full Lebesgue measure then it is residual, but the converse may not hold. Also, if λ² denotes the Lebesgue measure on the square and Ch(f) is the set of points (x,y) ∈ C(f) for which neither x nor y are asymptotically periodic, we show that λ²(C(f)) > 0 need not imply λ²(Ch(f)) > 0. We use these results to propose some plausible definitions...
Définition axiomatique de la mesure de Hausdorff
Deformation quantization and Borel's theorem in locally convex spaces
It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions...
Degré topologique pour les fonctions convexes.
El objeto de esta nota es presentar una noción del grado topológico para funciones reales convexas sci (semicontinuas inferiormente) basándose en la teoría del grado introducida por F. Browder.
Dendroids and their endpoints
Denjoy integral and Henstock-Kurzweil integral in vector lattices. II
In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.
Denjoy integral and Henstock-Kurzweil integral in vector lattices. I
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.
Dense chaos
According to A. Lasota, a continuous function from a real compact interval into itself is called generically chaotic if the set of all points , for which and , is residual in . Being inspired by this definition we say that is densely chaotic if this set is dense in . A characterization of the generically chaotic functions is known. In the paper the densely chaotic functions are characterized and it is proved that in the class of piecewise monotone maps with finite number of pieces the...
Denseness of domains of differential operators in Sobolev spaces.
Density Continuity versus Continuity.
Density covers
Density theorems for local minimizers of area-type functionals
Der Beweis des Fundamentalsatzes der Integralrechnung: ................
Der Greensche Satz
Der Kolmogroff'sche Darstellung-Satz bei halbstetigen Funktionen.
Der Satz von Osgood-Hartogs für reelle Funktionen.