Related papers: On self-affine sets
In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…
In this paper, we discuss the self-shrinking systems in higher codimensional spaces. We mainly obtain several Bernstein type results and a sharp growth estimate.
We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…
This paper is a survey (may be incomplete) on partial Nambu-Poisson structures in infinite dimension, mainly in the convenient setting. These ones can be seen as a generalization of both partial Poisson and Nambu-Poisson structures. We also…
In this article we survey some of the recent developments in the structure theory of set addition.
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
In this survey article we discuss about possible generalizations of Anosov representations in the affine setting and their consequences.
We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…
The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.
In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications.
This paper is meant to be a short review and summary of recent results on the structure of finite and affine classical W-algebras, and the application of the latter to the theory of generalized Drinfeld-Sokolov hierarchies.
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset…
A classification of (countable) direct limits of finite dimensional involution simple associative algebras over an algebraically closed field of arbitrary characteristic is obtained. This also classifies the corresponding dimension groups.…
The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.
It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity…
We consider a class of planar self-affine sets which we call "box-like". A box-like self-affine set is the attractor of an iterated function system (IFS) of affine maps where the image of the unit square, [0,1]^2, under arbitrary…
We give an explicit construction of a large subset of F^n, where F is a finite field, that has small intersection with any affine variety of fixed dimension and bounded degree. Our construction generalizes a recent result of Dvir and Lovett…
The sub-additive pressure function $P(s)$ for an affine iterated function system (IFS) and the affinity dimension, defined as the unique solution $s_0$ to $P(s_0)=1$, were introduced by K. Falconer in his seminal 1988 paper on self-affine…
We investigate a formula of K. Falconer which describes the typical value of the generalised R\'enyi dimension, or generalised $q$-dimension, of a self-affine measure in terms of the linear components of the affinities. We show that in…
We extend the result of K. Karlander [Math. Scand. 80 (1997)] regarding finite dimensionality of spaces of absolutely convergent Fourier transforms.