Die Hausdorff-Dimension von Mengen reeller Zahlenfolgen.
Die Obstruktion zur strengen Lokalisierbarkeit eines Maszraumes.
Die Verallgemeinerungen des Darstellungssatzes von F. Riesz und ihre Anwendungen.
Dieudonné-type theorems for lattice group-valued -triangular set functions
Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.
Diferenciación de medidas vectoriales en semi-μ-espacios de Lusin.
Difference functions of periodic measurable functions
We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets (e.g. measurable...
Difference of general integral means.
Differences of random Cantor sets and lower spectral radii
Differentation along algebras.
Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem
A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally finite G-perimeter....
Differentiability and rigidity theorems.
Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)
In this paper we introduce a concept of Schauder basis on a self-similar fractal set and develop differential and integral calculus for them. We give the following results: (1) We introduce a Schauder/Haar basis on a self-similar fractal set (Theorems I and I'). (2) We obtain a wavelet expansion for the L²-space with respect to the Hausdorff measure on a self-similar fractal set (Theorems II and II'). (3) We introduce a product structure and derivation on a self-similar fractal set (Theorem III). (4) We give the Taylor expansion theorem on a fractal set (Theorem IV and IV'). (5) By use of the Taylor expansion for wavelet functions, we introduce basic functions, for example, exponential and trigonometrical functions, and discuss the relationship between the usual and introduced corresponding special functions (Theorem V). (6) Finally we discuss the relationship between the wavelet functions and the generating functions...
Differentiation of implicit functions and Steinhaus' theorem in topological measure spaces
Differentiation of integrals [Abstract of thesis]
Differentiation of measures.
Differentiation through starlike sets in
Diffusion and propagation problems in some ramified domains with a fractal boundary
This paper is devoted to some elliptic boundary value problems in a self-similar ramified domain of with a fractal boundary. Both the Laplace and Helmholtz equations are studied. A generalized Neumann boundary condition is imposed on the fractal boundary. Sobolev spaces on this domain are studied. In particular, extension and trace results are obtained. These results enable the investigation of the variational formulation of the above mentioned boundary value problems. Next, for homogeneous...
Digit sets of integral self-affine tiles with prime determinant
Let M ∈ Mₙ(ℤ) be expanding such that |det(M)| = p is a prime and pℤⁿ ⊈ M²(ℤⁿ). Let D ⊂ ℤⁿ be a finite set with |D| = |det(M)|. Suppose the attractor T(M,D) of the iterated function system has positive Lebesgue measure. We prove that (i) if D ⊈ M(ℤⁿ), then D is a complete set of coset representatives of ℤⁿ/M(ℤⁿ); (ii) if D ⊆ M(ℤⁿ), then there exists a positive integer γ such that , where D₀ is a complete set of coset representatives of ℤⁿ/M(ℤⁿ). This improves the corresponding results of Kenyon,...
Digitální sluneční hodiny, paradoxní množiny a Vituškinova hypotéza
Dimension and Entropy of a Non-ergodic Markovian Process and its Relation to Rademacher Riesz Products.