Characterization of moment multisequences by a variation of positive definiteness.
Characterization of perfect involution groups.
Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one.
Completely monotone functions of finite order and Agler's conditions
Motivated by some structural properties of Drury-Arveson d-shift, we investigate a class of functions consisting of polynomials and completely monotone functions defined on the semi-group ℕ of non-negative integers, and its operator-theoretic counterpart which we refer to as the class of completely hypercontractive tuples of finite order. We obtain a Lévy-Khinchin type integral representation for the spherical generating tuples associated with such operator tuples and discuss its applications.
Completely positive maps on Coxeter groups, deformed commutation relations, and operator spaces.
Complex Hadamard matrices and the spectral set conjecture.
By analyzing the connection between complex Hadamard matrices and spectral sets, we prove the direction "spectral ⇒ tile" of the Spectral Set Conjecture, for all sets A of size |A| ≤ 5, in any finite Abelian group. This result is then extended to the infinite grid Zd for any dimension d, and finally to Rd.
Construction of positive definite functions
Convolution Quotients of Nonnegative Functions.
Convolution Semigroups and Resolvent Families of Measures on Hypergroups.