We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Recently Landau and Diffie gave in a series of articles in the Notices of the American Mathematical Society [DL02, Lan01, Lan00a, Lan00b] and in the American Mathematical Monthly [Lan04] excellent expositions on how the theory of multivariable polynomials are used in cryptography. However they covered only half of the story. They covered only the theory of polynomials in symmetric or secret cry...

A no®el geometric terrain methodology was recently presented for finding all physically rele®ant solutions and singular points to chemical process simulation problems based on intelligently mo®ing along special integral cur®es of the gradient ®ector field to guide both uphill and downhill mo®ement. The terrain methodology is extended here to include multi®ariable problems and integral cur®e bif...

In this paper we solve moment problems for Poisson transforms and, more generally, for completely positive linear maps on unital C∗-algebras generated by “universal” row contractions associated with F+n , the free semigroup with n generators. This class of C ∗-algebras includes the Cuntz-Toeplitz algebra C∗(S1, . . . , Sn) (resp. C ∗(B1, . . . , Bn)) generated by the creation operators on the f...