Functional equations stemming from probability theory

Some functional equations originating from number theory

If the answer is affirmative, the functional equation for homomorphisms is said to be stable in the sense of Hyers and Ulam because the first result concerning the stability of functional equations was presented by Hyers. Indeed, he has answered the question of Ulam for the case where G1 and G2 are assumed to be Banach spaces (see [8]). We may find a number of papers concerning the stability re...

Functional Equations and Characterization of Probability Distributions

Functional Inequalities in Analysis and Probability Theory

My research is in Functional Analysis (AMS classification 46), Operator Theory (47), Global Analysis (58), Probability Theory (60), and Combinatorics (05). Most of what I do relates to functional inequalities, often arising in mathematical physics, in many different contexts. Much of my recent work is in and around free probability theory, an important and relatively new field at the confluence...

Effective Maxwell Equations from Time-dependent Density Functional Theory

The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.

Quantum Probability from Decision Theory?

In a recent paper, Deutsch [1] claims to derive the “probabilistic predictions of quantum theory” from the “non-probabilistic axioms of quantum theory” and the “non-probabilistic part of classical decision theory.” We show that his derivation fails because it includes hidden probabilistic assumptions.