Abstract This short note is concerned with various operator representations of frames in a Hilbert space $${{{\mathcal {H}}}}.$$ H . While it known that only very special can be represented the form $$\{ T^n \varphi \}_{n=0}^\infty $$ { <m...

Decay rates for the sequence of eigenvalues of positive and compact integral operators have been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square integrable functions on the unit sphere and generated by a kernel satisfying a Hölder type assumption defined by average operators. In the approach to be presented...

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).