Darboux property for functions of several variables
Decomposable functions of several variables.
Decomposition of smooth functions of two multidimensional variables
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...
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...
Denseness of domains of differential operators in Sobolev spaces.
Der Greensche Satz
Der Kolmogroff'sche Darstellung-Satz bei halbstetigen Funktionen.
Derivatives are Borel functions.
Deux exemples de fonctions non mesurables
Diagonals of separately continuous functions of variables with values in strongly -metrizable spaces
We prove the result on Baire classification of mappings which are continuous with respect to the first variable and belongs to a Baire class with respect to the second one, where is a -space, is a topological space and is a strongly -metrizable space with additional properties. We show that for any topological space , special equiconnected space and a mapping of the -th Baire class there exists a strongly separately continuous mapping with the diagonal . For wide classes of spaces...
Diameter of Sets and Measure of Sumsets.
Die Dehnsche Zerlegungsinvariante für hyperbolische Polyederbausteine.
Die gleichmässige Convergenz von Functionen mehrerer Veränderlichen zu den dadurch sich ergebenden Grenzwerthen, dass einige derselben constanten Werthen sich nähern
Diferenciální počet II [Book]
Differences of two semiconvex functions on the real line
It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which and for each ). Further, for each modulus , we characterize the class of functions on which can be written as , where and are semiconvex with modulus (for some ) using a new notion of...
Differentiability from the representation formula and the Sobolev-Poincaré inequality
In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.
Differentiability of Minima of Non-Differentiable Functionals.
Differentiable Functions into Real Normed Spaces
In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].