Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMinkowskis question mark measure is UST--regular
84
0
0.0
(
0
)
Authors
Giorgio Mantica
Ask ChatGPT about the research
No Arabic abstract
We prove the recent conjecture that Minkowskis question mark measure is regular, in the sense of Ullman-Stahl-Totik.
rate research
Read More
Minkowskis question mark function is the distribution function of a singular continuous measure: we study this measure from the point of view of logarithmic potential theory and orthogonal polynomials. We conjecture that it is regular, in the sense of Ullman--Stahl--Totik and moreover it belongs to a Nevai class: we provide numerical evidence of the validity of these conjectures. In addition, we study the zeros of its orthogonal polynomials and the associated Christoffel functions, for which asymptotic formulae are derived. Rigorous results and numerical techniques are based upon Iterated Function Systems composed of Mobius maps.
We study the one-dimensional projection of the extremal Gibbs measures of the two-dimensional Ising model, the Schonmann projection. These measures are known to be non-Gibbsian at low temperatures, since their conditional probabilities as a function of the two-sided boundary conditions are not continuous. We prove that they are g-measures, which means that their conditional probabilities have a continuous dependence on one-sided boundary condition.
There are many tests for determining the convergence or divergence of series. The test of Raabe and the test of Betrand are relatively unknown and do not appear in most classical courses of analysis. Also, the link between these tests and regular variation is seldomly made. In this paper we offer a unified approach to some of the classical tests from a point of view of regular varying sequences.
We prove that every pair of exponential polynomials with imaginary frequencies generates a Poisson-type formula.
A space of pseudoquotients $mathcal P (X,S)$ is defined as equivalence classes of pairs $(x,f)$, where $x$ is an element of a non-empty set $X$, $f$ is an element of $S$, a commutative semigroup of injective maps from $X$ to $X$, and $(x,f) sim (y,g)$ if $gx=fy$. In this note we assume that $(X,Sigma,mu)$ is a measure space and that $S$ is a commutative semigroup of measurable injections acting on $X$ and investigate under what conditions there is an extension of $mu$ to $mathcal P (X,S)$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
