Abstract We consider the action of Mandelbrot multiplicative cascades on probability measures supported a symbolic space. For general measures, we obtain almost sharp criterion non-degeneracy limiting measure; it relies lower and upper Hausdorff dimensions measure entropy random weights. also bounds for packing measure. When original is Gibbs associated with potential certain modulus continuity...

We prove by elementary methods the following generalization of a theorem due to Gleason, Kahane, and Żelazko. Let A be a real algebra with unit 1 such that the spectrum of every element in A is bounded and let φ : A→ C be a linear map such that φ(1) = 1 and (φ(a))2 + (φ(b))2 = 0 for all a, b in A satisfying ab = ba and a2 + b2 is invertible. Then φ(ab) = φ(a)φ(b) for all a, b in A. Similar resu...

In this article we obtain 2 generalizations of the well known Gleason-Kahane-Z̀elazko Theorem. We consider a unital Banach algebra A, and a continuous unital linear mapping φ of A into Mn(C) – the n × n matrices over C. The first generalization states that if φ sends invertible elements to invertible elements, then the kernel of φ is contained in a proper two sided closed ideal of finite codimen...

for all z1; . . . ; zn 2 C and all n 1 . The constant p 2 is shown to be the best possible. The method of proof relies upon a combinatorial argument, Taylor expansion, and the central limit theorem. The result is additionally strengthened by showing that the underlying functions are Schur-concave. The proof of this fact uses a result on multinomial distribution of Rinott, and Schur’s propositio...

Several inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the well-known estimates for subnormal random variables, see [9], the third one is a consequence of a certain Gaussian-Jensen’s majorization technique, see [6], and the f...

Abstract We prove stronger variants of a multiplier theorem Kislyakov. The key ingredients are based on ideas Kislyakov and the Kahane–Salem–Zygmund inequality. As by-product, we show various theorems for spaces trigonometric polynomials n -dimensional torus $\mathbb {T}^n$ or Boolean cubes $\{-1,1\}^N$ . Our more abstract approach local Banach space theory has advantage that it allows to consi...

In this paper we study ultraflat sequences (Pn) of unimodular polynomials Pn ∈ Kn in general, not necessarily those produced by Kahane in his paper [Ka]. We examine how far is a sequence (Pn) of unimodular polynomials Pn ∈ Kn from being conjugate reciprocal. Our main results include the following. Theorem. Given a sequence (εn) of positive numbers tending to 0, assume that (Pn) is a (εn)-ultraf...

Running head: Multimodal Imaging of Eating Reflex Seizures Thomas Blauwblomme, MSc, Philippe Kahane, MD PhD, Lorella Minotti MD, Frédéric Grouiller, PhD, Alexandre Krainik, MD PhD, Laurent Vercueil, MD PhD, Stéphan Chabardès, MD, Dominique Hoffmann, MD, Olivier David, PhD 1 INSERM, U836, Grenoble Institute of Neuroscience, France 2 Université Joseph Fourier, Grenoble, France 3 Department of Neu...

We extend the Khinchin–Kahane inequality to an arbitrary abelian metric group G . In the special case where G is normed, we prove a refinement which is sharp and which extends the sharp version for Banach spaces. We also provide an alternate proof for normed metric groups as a consequence of a general “transfer principle”. This transfer principle has immediate applications to stochastic inequal...