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## Publications

Publications (6)

The Modular group ? is the most well-known discrete group with many applications. This work investigates some subgraphs of the subgroup ?3, defined by {(ab cd)??:ab+cd ?0 (mod 3)}. In [1], the subgraph F1,1 of the subgroup ?3 ? ? is studied, and Fibonacci numbers are obtained by means of the subgraph of F1,1. In this paper, we give a generalization...

In this work, we study suborbital graphs for the congruence subgroup Γ0(nh) acting on the subset ℚ^(h) and it is proved that the subgraph F1,n gives very useful number theoretical results such as Fibonacci numbers and some inequalities.

In this paper, for an isometric strongly continuous linear representation denoted by α of the topological group of the unit circle in complex Banach space, we study an integral representation for Abel Poisson mean Arα(x) of the Fourier coefficients family of an element x, and it is proved that this family is Abel-Poisson summable to x. Finally, we...

Let A denote the generator of a strongly continuous periodic one-parameter group of bounded linear operators in a complex Banach space H. In this work, an analog of the resolvent operator which is called quasi-resolvent operator and denoted by Rλ is defined for points of the spectrum, some equivalent conditions for compactness of the quasi-resolven...

Let H be a complex Banach space, T be the topological group of the unit circle with respect to the Euclidean topology,
α be a strongly continuous isometric linear representation of T in H,
{
F
k
α
}
k
∈
ℤ
be the family of Fourier coefficients with respect to α, and
{
σ
k
α
}
k
∈
ℤ
be Cesaro means of the family
{
F
k
α
}
k
∈
ℤ
. In...

In this work, a family {P-n(alpha)}(n is an element of Z) of orthogonal projections on a complex Hilbert space H is defined by means of a periodic continuous unitary representation alpha of the topological group (R,+) on H, and some properties of this family are given.