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...

In this paper, we consider the non-homogeneous wave equation generated by Bessel operator. We prove existence and uniqueness of solution The representation is given. obtained a priori estimates in Sobolev type space. This problem was firstly considered work M. Assal [1] setting Bessel-Kingman hypergroups. technique used based on convolution theorem related estimates. Here, use different approac...

‎Frames generalize orthonormal bases and allow representation of all the elements of the space‎. ‎Frames play significant role in signal and image processing‎, ‎which leads to many applications in informatics‎, ‎engineering‎, ‎medicine‎, ‎and probability‎. ‎In this paper‎, ‎we introduce the concepts of operator frame for the space $End_{mathcal{A}}^{ast}(mathcal{H})$ of all adjointable operator...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.