the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

using a bessel generalized translation, we obtain an analog of titchmarsh's theorem for the bessel transform for functions satisfying the lipschitz condition in the space $mathrm{l}_{p,alpha}(mathbb{r}_{+})$, where $alpha>-frac{1}{2}$ and $1

If B < ∞ we call F = {fi}i∈I a Bessel sequence with Bessel bound B. If 0 < A ≤ B < ∞, then {fi}i∈I is a frame for K. If K 6= H we call {fi}i∈I a frame sequence in H. The largest A and the smallest B satisfying the above inequalities are called the optimal lower and upper frame bound and will be denoted A(F) and B(F) respectively. If A = B = λ we call this a λ-tight frame and if λ = 1 it is call...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

in this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of hilbert $c^ast-$ modules and vice versa, then we consider tensor products of g-bessel multipliers, bessel multipliers and bessel fusion multipliers in hilbert $c^ast-$modules. moreover, we obtain so...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...

The (n 1)th Bessel polynomial is represented by an exponential generating function derived from the number of returns to 0 of a sequence with 2n increments of 1 which starts and ends at 0. AMS 1991 subject classi cation. Primary: 05A15. Secondary: 33C10, 33C45. It is well known [21, x3.71 (12)],[6, (7.2(40)] that the McDonald function or Bessel function of imaginary argument K (x) := 1 2 x 2 Z ...