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...

We investigate ultra-broadband wavelength converters based on cascaded second-harmonic generation and difference frequency generation using Bessel-chirped gratings (BCGs) in lithium niobate waveguides, and compare them to the ones using uniform grating and segmented grating, respectively. For the same length and power, the BCGs show broader bandwidth than the other two types of grating. The rip...

We report on the existence of nondiffracting Bessel surface plasmon polaritons (SPPs), advancing at either superluminal or subluminal phase velocities. These wave fields feature deep subwavelength FWHM, but are supported by high-order homogeneous SPPs of a metal/dielectric (MD) superlattice. The beam axis can be relocated to any MD interface, by interfering multiple converging SPPs with control...

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 ...

In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

for all f ∈ H.A and B are called frame bounds.The sequence is called a tight frame if A = B. The sequence is called Bessel if the second inequality above holds. In this case, B is called the Bessel bound. Frames were first introduced by Duffin and Schaeffer [1] in the context of nonharmonic Fourier series, and today they have applications in a wide range of areas. A frame can be considered as a...

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.