On locally compact semitopological graph inverse semigroups
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 1
Abstract
In this paper we investigate locally compact semitopological graph inverse semigroups. Our main result is the following: if a directed graph E is strongly connected and has finitely many vertices, then any Hausdorff shift-continuous locally compact topology on the graph inverse semigroup G(E) is either compact or discrete. This result generalizes results of Gutik and Bardyla who proved the above dichotomy for Hausdorff locally compact shift-continuous topologies on polycyclic monoids P1 and Pλ, respectively.
Authors and Affiliations
S. O. Bardyla
Meromorphic function sharing three sets with its shift, q-shift, q-difference and analogous operators
Using the notion of weighted sharing of three sets we deal with the uniqueness problem of meromorphic function with its shift, q-shift, q-difference and analogous operator. A handful number of examples have been provided...
Complete biorthogonal systems of Bessel functions
Let ν≥−1/2 and (ρk)k∈N be a sequence of nonzero complex numbers such that ρ2k≠ρ2m for k≠m. We prove that if the system {xρk−−−√Jν(xρk):k∈N} of Bessel functions of the first kind of index ν≥−1/2 is exact (i.e. complete an...
Distance between a maximum modulus point and zero set of an analytic function
Let f be an analytic function in the disk DR={z∈C:|z|≤R}, R∈(0,+∞]. We call a point w∈DR a maximum modulus point of f if |f(w)|=M(|w|,f), where M(r,f)=max{|f(z)|:|z|=r}. Denote by d(w,f) the distance between a maximum mo...
On belonging of entire Dirichlet series to a modified generalized convergence class
For entire Dirichlet series F(s)=∑+∞n=0anesλn we found conditions on an, λn and on positive functions α and β continuous increasing to +∞ on [0,+∞) are found, under which the condition ∫+∞σ01β(σ)α(1σlnM(σ,F))dσ≤+∞ is equ...
Uniqueness of solution for the inverse problem of finding two minor coefficients in a semilinear time fractional telegraph equation
We find sufficient conditions of the uniqueness of a solution for the inverse problem of determining two continuous minor coefficients in a semilinear time fractional telegraph equation under two integral overdeterminati...