منابع مشابه
ON THE SINGULARITIES OF THE CONTINUOUS JACOBI TRANSFORM WHEN a + ß = 0
Let a,ß > -1 and Pla'3)(x) = (l-x)a(l+x)ßp[a'a){x), where Pjf (x) is the Jacobi function of the first kind, A > —(a + ß + l)/2, and -1 < i < 1. Let r the integral exists. It is known that for a + •>-Ä4r'<",')(*-i),£Ä<-> *J o whenever ß = 0, we have /(*) = lim 4 f fC« (x l) PÍÍ$A-*)\ . . r2(A + i/2) X sin 7rA^-:-L_¡-d\ w in J, r(A-ra + l/2)F(A + ^ + l/2) almost everywhere in [—1,1], In this pape...
متن کاملTHE BIG q-JACOBI FUNCTION TRANSFORM
Abstract. We give a detailed description of the resolution of the identity of a second order q-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The q-difference operator and the two choices of Hilbert spaces naturally arise from harmonic analysis on the quantum group SUq(1, 1) and SUq(2). The spectral analysis associated to SUq(1, 1) leads to...
متن کاملThe absolutely continuous spectrum of Jacobi matrices
I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrödinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme...
متن کاملSome Results for the Jacobi-Dunkl Transform in the Space $L^{p}(mathbb{R},A_{alpha,beta}(x)dx)$
In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.
متن کاملTRANSMUTATION KERNELS FOR THE LITTLE q-JACOBI FUNCTION TRANSFORM
The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel relating little q-Jacobi function transforms for different parameter sets. A product formula for the dual transmutation kernel is obtained. For the inverse transform the transmutation kernel is given as a 3φ2-series, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1985
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171285000357