Let Ω be a bounded domain in C. Let R(Ω) (usually A(Ω) or H(Ω)) be a ring of holomorphic functions that contains the polynomials, and let p = (p1, . . . , pn) be a point in Ω. Recall the Gleason problem, cf. [8]: is the maximal ideal in R(Ω) consisting of functions vanishing at p, generated by the coordinate functions (z1 − p1), . . . , (zn − pn) ? One says that a domain Ω has the Gleason R-pro...

Quantum processes cannot be reduced, in a nontrivial way, to classical without specifying the context description of measurement procedure. This requirement is implied by Kochen--Specker theorem outcome-deterministic case and, more generally, Gleason theorem. The latter establishes that there only one noncontextual model compatible with quantum theory, trivially identifies state state. However,...

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.

A substantial body of evidence indicates that utilitarian judgments (favoring the greater good) made in response to difficult moral dilemmas are preferentially supported by controlled, reflective processes, whereas deontological judgments (favoring rights/duties) in such cases are preferentially supported by automatic, intuitive processes. A recent neuroimaging study by Kahane et al. challenges...

Quadratic residue codes are some of the brightest gems of coding theory. Their facets reeect many topics: quadratic residues and reciprocity; multiply transitive and sporadic simple groups; lattices; group representations; and block designs and Hadamard matrices. They provide the only perfect codes for prime-power sized alphabets correcting more than one error, and some are prototypes of extrem...

One of the most resolute dichotomies in modern and contemporary study religion is that between good/bad religions. The bases for making such judgments are fluid, but outcome generally recognizable; “good” religions good religious practitioners adhere to expectations norms bourgeois modern. reasons endurance dichotomy historical, rooted rise as an academic discipline, globally United States; eco...

A substantial body of evidence indicates that utilitarian judgments (favoring the greater good) made in response to difficult moral dilemmas are preferentially supported by controlled, reflective processes, whereas deontological judgments (favoring rights/duties) in such cases are preferentially supported by automatic, intuitive processes. A recent neuroimaging study by Kahane et al. challenges...

We extend Kahane-Khinchin type inequalities to the case p > −2. As an application we verify the slicing problem for the unit balls of finite-dimensional spaces that embed in Lp, p > −2.

Let Pn(z) = ∑n k=0 ak,nz k ∈ C[z] be a sequence of unimodular polynomials (|ak,n| = 1 for all k, n) which is ultraflat in the sense of Kahane, i.e., lim n→∞ max |z|=1 ∣

The probelm of generalizing Gleason’s theorem to the non separable case arose in correspondence with Paul Chernoff. I am very grateful to him for suggesting this charming problem to me. Let H be a Hilbert space. The coefficient field K of H can be either the reals or the complexes. We let P(H) denote the collection of all closed subspaces of H. A Gleason measure on H is a map μ : P(H) → [0, 1] ...