Under minimal Kahane–Peyrière integrability, the Fourier dimension of a scalar dyadic Mandelbrot cascade pushed onto any fixed nondegenerate C² arc or Jordan curve equals A_loc(W), the same explicit endpoint value as the canonical circle.
Title resolution pending
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
representative citing papers
Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
A new restriction theorem is established that uses L^q-dimensions to obtain a continuum of Fourier restriction estimates recovering Stein-Tomas at q=∞ via complex interpolation, with improvements shown for certain multifractal measures.
Fourier dimension of the graph of fBM with H ≥ 1/2 is a.s. 1, established via a new combinatorial integration by parts formula combined with Faà di Bruno's formula and strong local nondeterminism.
Fourier dimension of canonical Mandelbrot cascade measures equals the energy exponent almost surely under the minimal Kahane-Peyrière integrability condition.
citing papers explorer
-
Exact Fourier dimensions of dyadic Mandelbrot cascades on curves of nonvanishing curvature under minimal integrability
Under minimal Kahane–Peyrière integrability, the Fourier dimension of a scalar dyadic Mandelbrot cascade pushed onto any fixed nondegenerate C² arc or Jordan curve equals A_loc(W), the same explicit endpoint value as the canonical circle.
-
Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability
Under minimal Kahane-Peyriere integrability, dyadic Mandelbrot cascades satisfy dim_F(mu) = dim_E(mu) = dim_2(mu) = D_E(X) almost surely on non-extinction, with explicit sup formulas for scalar and circle cases.
-
Fourier restriction estimates based on $L^q$-dimensions: beyond Stein--Tomas
A new restriction theorem is established that uses L^q-dimensions to obtain a continuum of Fourier restriction estimates recovering Stein-Tomas at q=∞ via complex interpolation, with improvements shown for certain multifractal measures.
-
Fourier dimension of the graph of fractional Brownian motion with $H \ge 1/2$
Fourier dimension of the graph of fBM with H ≥ 1/2 is a.s. 1, established via a new combinatorial integration by parts formula combined with Faà di Bruno's formula and strong local nondeterminism.
-
Fourier Dimensions of Mandelbrot Cascades under Minimal Integrability
Fourier dimension of canonical Mandelbrot cascade measures equals the energy exponent almost surely under the minimal Kahane-Peyrière integrability condition.