Some Extension of the Bessel - Type Orthogonalpolynomials
نویسنده
چکیده
We consider the perturbation of the classical Bessel moment functional by the addition of the linear functional M 0 (x) + M 1 0 (x), where M 0 and M 1 2 IR. We give necessary and suucient conditions in order for this functional to be a quasi-deenite functional. In such a situation we analyze the corresponding sequence of monic orthogonal polynomials B ;M0;M1 n (x). In particular, a hypergeometric representation (4 F 2) for them is obtained. Furthermore, we deduce a relation between the corresponding Jacobi matrices, as well as the asymptotic behavior of the ratio B ;M0;M1 n (x)=B n (x), outside of the closed contour containing the origin and the diierence between the new polynomials and the classical ones, inside .
منابع مشابه
Duality of $g$-Bessel sequences and some results about RIP $g$-frames
In this paper, first we develop the duality concept for $g$-Bessel sequences and Bessel fusion sequences in Hilbert spaces. We obtain some results about dual, pseudo-dual and approximate dual of frames and fusion frames. We also expand every $g$-Bessel sequence to a frame by summing some elements. We define the restricted isometry property for $g$-frames and generalize some resu...
متن کاملEstimates for the Generalized Fourier-Bessel Transform in the Space L2
Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.
متن کاملSome Random times and Martingales Associated with Bes0(δ) Processes (0 < Δ < 2)
In this paper, we study Bessel processes of dimension δ ≡ 2(1 − μ), with 0 < δ < 2, and some related martingales and random times. Our approach is based on martingale techniques and the general theory of stochastic processes (unlike the usual approach based on excursion theory), although for 0 < δ < 1, these processes are even not semimartingales. The last time before 1 when a Bessel process hi...
متن کاملBessel multipliers on the tensor product of Hilbert $C^ast-$ modules
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...
متن کاملMultipliers of continuous $G$-frames in Hilbert spaces
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.
متن کامل