in this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. we establishthe orthogonality relations for square integrable representationsof homogeneous spaces which give rise to the existence of aunique self adjoint positive operator on the set of admissiblewavelets. finally, we show that this operator is a constant multiple of identity operator...

We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log k). This method yields o(k)-competitive algorithms solving the randomized k-server problem, for some special underlying metric spaces, e.g. HSTs of"small"heigh...

For an open and dense subset in the Teichmüller space, we introduce a coordinate system which is well-behaved under the action of the mapping class group. Surprisingly, the coordinates involve the K-theory of certain operator algebras. Our approach is an interplay of the noncommutative geometry with the Teichmüller theory, which opens new vistas of the both.

In the theory of generalized metric spaces, the notion of knetworks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every LaSnev space, as well as, every space dominated by LaSnev spaces has a a-compact-finite knetwork. We recall that every space has a compa...

This note provides a computation of the bordism groups of K-Witt spaces for fields K with characteristic 2. We provide a complete computation for the unoriented bordism groups. For the oriented bordism groups, a nearly complete computation is provided as well a discussion of the difficulty of resolving a remaining ambiguity in dimensions equivalent to 2 mod 4. This corrects an error in the char...

In this paper, we show that the ball measure of noncompactness of a modular space Xp is equal to the limit of its K -widths when p is a left continuous, s-convex modular function, without any ~rcondition. We also obtain a similar result for SF-spaces, when the SF-norm N is uniformly continuous. 1991 Mathematics Subject Classification: 46E30, 46A50, 46B99 1. Notation and definitions Throughout t...