Nonlinear dynamical systems and classical orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Q-Hermite Polynomials and Classical Orthogonal Polynomials
We use generating functions to express orthogonality relations in the form of q-beta integrals. The integrand of such a q-beta integral is then used as a weight function for a new set of orthogonal or biorthogonal functions. This method is applied to the continuous q-Hermite polynomials, the Al-Salam-Carlitz polynomials, and the polynomials of Szegő and leads naturally to the Al-Salam-Chihara p...
متن کاملQuantum-classical transition in nonlinear dynamical systems.
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive semidefiniteness of the density matrix. The nature of the violation suggests a classification of dynamical systems based on classical-quantum correspondence; we show that this can be used to identify when environmental interaction (decoherence) will be unsuccessful in inducing the quantum-classical tran...
متن کاملClassical Orthogonal Polynomials as Moments
We show that the Meixner, Pollaczek, Meixner-Pollaczek and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures. We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials. Running Title: Generating Functions
متن کاملClassical 2-orthogonal polynomials and differential equations
We construct the linear differential equations of third order satisfied by the classical 2orthogonal polynomials. We show that these differential equations have the following form: R4,n(x)P (3) n+3(x)+R3,n(x)P ′′ n+3(x)+R2,n(x)P ′ n+3(x)+R1,n(x)Pn+3(x)=0, where the coefficients {Rk,n(x)}k=1,4 are polynomials whose degrees are, respectively, less than or equal to 4, 3, 2, and 1. We also show tha...
متن کاملExtremal problems, inequalities, and classical orthogonal polynomials
In this survey paper we give a short account on characterizations for very classical orthogonal polynomials via extremal problems and the corresponding inequalities. Beside the basic properties of the classical orthogonal polynomials we consider polynomial inequalities of Landau and Kolmogoroff type, some weighted polynomial inequalities in L2-norm of Markov-Bernstein type, as well as the corre...
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: Journal of Mathematical Physics
سال: 1997
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.531990