For a delta operator aD − bD we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D − 1 2D 2 we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions νt, t > 0, for which {yn(t)}, the Bessel polynomials at t, is the moment ...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

In this paper we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller numbe...

The notion of frame in a Banach spaces E via semi-inner product was introduced and studied in [16]. In this paper, we give a characterisation for SIP-II Ed-Bessel sequence to be SIP-II Ed-frame. Also, a necessary and sufficient condition for the finite sum of SIP-II Ed frame for E to be a SIP-II Ed frame for E has been obtained. Further, a sufficient condition for the stability of finite sum of...

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...

The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two obser...

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...