On the hausdorff dimensions of distance sets
WebThere is also a neat construction of Salem sets (sets that have equal Fourier and Hausdorff dimensions) via results on the almost sure decay of Fourier transforms of certain measures on trajectories of Brownian motion. WebIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. …
On the hausdorff dimensions of distance sets
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WebThe Mumford–Shah functional is a functional that is used to establish an optimality criterion for segmenting an image into sub-regions. An image is modeled as a piecewise-smooth function. The functional penalizes the distance between the model and the input image, the lack of smoothness of the model within the sub-regions, and the length of the boundaries … WebIn mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff. For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a …
Web18 de out. de 2024 · The main topics concern applications of the Fourier transform to geometric problems involving Hausdorff dimension, such as Marstrand type projection … Web17 de mar. de 2016 · In this paper, we replace the Hausdorff dimension on the left hand side of the first inequality above by the lower Minkowski dimension and replace the Lebesgue measure of the set of translates by a Hausdorff measure on a set of sufficiently large ... On the Hausdorff dimensions of distance sets, Mathematika 32 (1985), …
Web8 de nov. de 2024 · We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than $1$, improving recent estimates of Keleti and ... Web3 de jun. de 2024 · We prove that if α ∈ (0, 1/2], then the packing dimension of a set E ⊂ ℝ2 for which there exists a set of lines of dimension 1 intersecting E in Hausdorff …
Web16 de dez. de 2024 · Abstract. We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for …
Web20 de jun. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors … detailed map of upper michiganWebAccording to a result of K. Falconer (1985), the setD(A)={ x−y ;x, y ∈A} of distances for a Souslin setA of ℝ n has positive 1-dimensional measure provided the Hausdorff … detailed map of vermont townsWeb2 de mar. de 2024 · The existence of Arnoux–Rauzy IETs with two different invariant probability measures is established in [].On the other hand, it is known (see []) that all Arnoux–Rauzy words are uniquely ergodic.There is no contradiction with our Theorem 1.1, since the symbolic dynamical system associated with an Arnoux–Rauzy word is in … chuna therapyWeb16 de dez. de 2024 · In dimensions $d=2$ or $3$, we obtain the first explicit estimates for the dimensions of distance sets of general Borel sets of dimension $d/2$; for example, we show that the set of... detailed map of west bengalWeb16 de dez. de 2024 · We establish the dimension version of Falconer's distance set conjecture for sets of equal Hausdorff and packing dimension (in particular, for Ahlfors-regular sets) in all ambient dimensions. In... Global Survey. In just 3 minutes help us understand how you see arXiv. chunbofoodWebOn the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers . × Close Log In. Log in with Facebook Log in … detailed map of veniceWebJ., Bourgain [1994] Hausdorff dimension and distance sets, Israel J. Math. 87, 193–201. J., Bourgain [1995] Some new estimates on oscillatory integrals, in Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton University Press, 83–112. chun board