LetG be a Hausdorff topological locally compact group. LetM(G) denote the Banach algebra of all complex and bounded measures on G. For all integers n ≥ 1 and all μ ∈ M(G), we consider the functional equations ∫ G f(xty)dμ(t) = ∑n i=1gi(x)hi(y), x,y ∈ G, where the functions f , {gi}, {hi}: G → C to be determined are bounded and continuous functions on G. We show how the solutions of these equati...

We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in R, n ≥ 1, is a σ-limit set for some continuous map.

The dynamic compact trie is a fundamental data structure for a wide range of string processing problems. In this paper, we report our recent work on succinct dynamic compact tries that stores a set of strings of total length n in O(n log σ) space supporting pattern matching and insert/delete operations in O((|P |/α)f(n)) time, where P is a pattern string, α = Θ(logσ n), and f(n) = O((log logn) ...

Let $\mathcal{C}(G)$ denote the Chabauty space of closed subgroups locally compact group $G$. In this paper, we first prove that $\mathcal{C} (\mathbb{Q}_p^\times)$ is a proper compactification $\mathbb{N}$, identified with set $N$ open finite index. Then identify $\mathcal{C}(\mathbb{Q}_p^\times) \smallsetminus N$ up to homeomorphism: e.g. for $p=2$, it Cantor on which 2 copies $\overline{\mat...

In this paper, the notions of countable S∗-compactness is introduced in L-topological spaces based on the notion of S∗-compactness. An S∗-compact L-set is countably S∗-compact. If L = [0, 1], then countable strong compactness implies countable S∗-compactness and countable S∗-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S∗-compact L-s...

The multivariate integer Chebyshev problem is to find polynomials with integer coefficients that minimize the supremum norm over a compact set in C. We study this problem on general sets, but devote special attention to product sets such as cube and polydisk. We also establish a multivariate analog of the Hilbert-Fekete upper bound for the integer Chebyshev constant, which depends on the dimens...