We derive simple explicit formula for the character of a cycle in the Connes’ (b, B)-bicomplex of cyclic cohomology and apply it to write formulas for the equivariant Chern character and characters of finitely-summable bounded Fredholm modules.

We combine the fundamental results of Breuillard, Green, and Tao (Publ Math Inst Hautes Études Sci 116:115–221, 2012) on structure approximate groups, together with “tame” arithmetic regularity methods based work authors Terry (J Eur Soc (JEMS) 24(2):583–621, 2022), to give a theorem for finite subsets A arbitrary groups G where has “small tripling” bounded VC-dimension: Roughly speaking, up sm...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

Given a (not necessarily discrete) proper metric space M with bounded geometry, we define a groupoid G(M). We show that the coarse Baum–Connes conjecture with coefficients, which states that the assembly map with coefficients for G(M) is an isomorphism, is hereditary by taking closed subspaces.

Two distributions over n-bit strings are (k, δ)-wise indistinguishable if no statistical test that observes k of the n bits can tell the two distributions apart with advantage better than δ. Motivated by secret sharing and cryptographic leakage resilience, we study the existence of pairs of distributions that are (k, δ)-wise indistinguishable, but can be distinguished by some function f of suit...