Inhomogeneous Diophantine approximation with general error functions
Let α be an irrational and φ: ℕ → ℝ⁺ be a function decreasing to zero. Let
Inhomogeneous self-similar sets and box dimensions
We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.
Injections de Sobolev probabilistes et applications
On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace , presque toute fonction appartient à tous les espaces , . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de formée d’harmoniques sphériques...
Inscribing closed non--lower porous sets into Suslin non--lower porous sets.
Inscribing compact non-σ-porous sets into analytic non-σ-porous sets
The main aim of this paper is to give a simpler proof of the following assertion. Let A be an analytic non-σ-porous subset of a locally compact metric space, E. Then there exists a compact non-σ-porous subset of A. Moreover, we prove the above assertion also for σ-P-porous sets, where P is a porosity-like relation on E satisfying some additional conditions. Our result covers σ-⟨g⟩-porous sets, σ-porous sets, and σ-symmetrically porous sets.
Inserting measurable functions precisely
A family of subsets of a set is called a -topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A -topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect -topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a -topological version of Katětov-Tong...
Integrability for the Dobrakov integral
Integrable cylinder functionals for an integral of Feynman-type
Integrable system of the heat kernel associated with logarithmic potentials
The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.
Integrace podle Hausdorffovy míry na hladké ploše
Integración de funciones con valores en un espacio localmente convexo respecto de medidas infinitas. II.
Integración de funciones con valores en un espacio localmente convexo respecto de medidas infinitas. III.
Integración de funciones con valores en un espacio localmente convexo respecto de medidas infinitas. I.
Integral de Riemann num espaço topológico geral
Integral extension procedures in weakly σ-complete lattice-ordered groups, II
Integral extension procedures in weakly σ-complete lattice-ordered groups, I
Integral extension with locally-integral seminorm
Integral formulas on projective space and the radon transform of Gindikin-Henkin-Polyakov.
We construct a variant of Koppelman's formula for (0,q)-forms with values in a line bundle, O(l), on projective space. The formula is then applied to a study of a Radon transform for (0,q)-forms, introduced by Gindikin-Henkin-Polyakov. Our presentation follows along the basic lines of Henkin-Polyakov [3], with some simplifications.
Integral functionals determined by their minima
Integral Geometry of the action fof ST(3) on the space E...