Riccati equations, zeroes and independece.
Bernoulli convolutions-an application of set theory in analysis
Metric properties of some planar sets
A metric property of some random functions
Fourier analysis and paths of brownian motion
Brownian motion, approximation of functions, and Fourier analysis
Measures in independent sets
Interpolation of additive functionals
Analytic sets in the theory of commutative semigroups
A problem about representations of countable, commutative semigroups leads to an analytic non-Borel set.
Approximation of smooth functions and covering properties of sets
Small subsets of finite abelian groups
Méthode probabiliste pour les moyennes de Fourier, sur un groupe fini, relatives à des mesures singulières.
Analysis on some linear sets
The note discusses a probabilistic method for constructing “small” sets, with regard to differentiable transformations and to quantitative measures of independence.
Topics on Kronecker sets
We obtain three theorems about transformation of sets of multiplicity onto Kronecker sets, by means of functions of various differentiability classes. The same method yields an improved theorem on the union of two Kronecker sets.
On the weak space and singular measures
We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak space; symmetric sets of constant ratio occur in an unexpected way.
On a class of semi-group algebras
On complexity of a set of norms in Banach spaces
Singularity of parabolic measures
Parabolic measure on domains of class Lip
Two problems on doubling measures.
Doubling measures appear in relation to quasiconformal mappings of the unit disk of the complex plane onto itself. Each such map determines a homeomorphism of the unit circle on itself, and the problem arises, which mappings f can occur as boundary mappings?
Smooth quasiregular maps with branching in
According to a theorem of Martio, Rickman and Väisälä, all nonconstant C-smooth quasiregular maps in , ≥3, are local homeomorphisms. Bonk and Heinonen proved that the order of smoothness is sharp in . We prove that the order of smoothness is sharp in . For each ≥5 we construct a C-smooth quasiregular map in with nonempty branch set.
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