Let A be a C*-algebra with an identity. Consider the completed tensor product A®A of A with itself with respect to the minimal or the maximal C*-tensor product norm. Assume that A: A —>A®A is a non-zero •-homomorphism such that (A ® t)A = (i ® A)A where / is the identity map. Then A is called a comultiplication on A . The pair (A, A) can be thought of as a 'compact quantum semi-group'. A left i...

Let P → M be a principal G-bundle. We construct well-defined substitutes for “Lebesgue measure” on the space A of connections on P and for “Haar measure” on the group G of gauge transformations. More precisely, we define algebras of “cylinder functions” on the spaces A, G, and A/G, and define generalized measures on these spaces as continuous linear functionals on the corresponding algebras. Bo...

Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the...

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures. Introduction A basic question in functional analysis is to find axioms for quantum groups, which ensure the existence of a Haar measure. In the compact case, this ...

In this paper we discuss general properties of geodesic surfaces that are (locally) biLipschitz homogeneous. In particular, we prove that they are locally doubling and there exists a special doubling measure analogous to the Haar measure for locally compact groups.

In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

Wavelet analysis as a p–adic spectral analysis Abstract New orthonormal basis of eigenfunctions for the Vladimirov operator of p–adic fractional derivation is constructed. The map of p–adic numbers onto real numbers (p–adic change of variable) is considered. p–Adic change of variable maps the Haar measure on p–adic numbers onto the Lebesgue measure on the positive semiline. p–Adic change of var...

Ergodic properties of p-adic transformations have been studied with respect to Haar measure. This paper extends the study of these properties to measures beyond Haar measure. Under these measures, coefficients do not appear in equal proportions. Adding a rational number that is not an integer then takes likely strings of coefficients to one of two unlikely strings of coefficients. It follows fr...

We study global reflection symmetries of almost periodic functions. In the non-limit periodic case, we establish an upper bound on the Haar measure of the set of those elements in the hull which are almost symmetric about the origin. As an application of this result we prove that in the nonlimit periodic case, the criterion of Jitomirskaya and Simon ensuring absence of eigenvalues for almost pe...