scholarly journals Characterization of classical type orthogonal polynomials

1994 ◽  
Vol 120 (2) ◽  
pp. 485-485 ◽  
Author(s):  
K. H. Kwon ◽  
L. L. Littlejohn ◽  
J. K. Lee ◽  
B. H. Yoo
Keyword(s):  
Orthogonal Polynomials ◽  
Classical Type

Differential Equation for Classical-Type Orthogonal Polynomials

1989 ◽  
Vol 32 (4) ◽  
pp. 404-411 ◽  
Author(s):  
A. Ronveaux ◽  
F. Marcellan
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Arbitrary Number ◽  
Order Differential Equation ◽  
Second Order ◽  
Classical Type ◽  
Dirac Mass ◽  
Second Order Differential Equation

AbstractThe second order differential equation of Littlejohn-Shore for Laguerre type orthogonal polynomials is generalized in two ways. First the positive Dirac mass can be situated at any point and secondly the weight can be any classical weight modified by an arbitrary number of Dirac distributions.

scholarly journals A characterization of the four Chebyshev orthogonal families

2005 ◽  
Vol 2005 (13) ◽  
pp. 2071-2079 ◽  
Author(s):  
E. Berriochoa ◽  
A. Cachafeiro ◽  
J. M. Garcia-Amor
Keyword(s):  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Linear Combinations ◽  
Classical Orthogonal Polynomial ◽  
Polynomial Sequences ◽  
Fixed Length ◽  
Constant Coefficients ◽  
Fourth Kind

We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences.

A characterization of some q-orthogonal polynomials

2006 ◽  
Vol 12 (3) ◽  
pp. 425-437 ◽  
Author(s):  
Somjit Datta ◽  
James Griffin
Keyword(s):  
Orthogonal Polynomials

Characterization of the LDL receptor in rat promegakaryoblasts in culture

1991 ◽  
Vol 11 (1) ◽  
pp. 15-21 ◽  
Author(s):  
Tracy J. Budd ◽  
Frank W. Hemming ◽  
Bruce Middleton
Keyword(s):  
Cell Biology ◽  
Receptor Cell ◽  
Low Density Lipoprotein ◽  
Ldl Receptor ◽  
Density Lipoprotein ◽  
Classical Type ◽  
Lysosomal Degradation ◽  
High Affinity ◽  
Ldl Binding

Rat promegakaryoblasts (RPM, a precursor platelet cell line) in culture exhibited a capacity to bind, take up and degrade125I-LDL. The low density lipoprotein (LDL) binding showed the following characteristics: (a) high affinity, (b) saturability, (c) specificity, (d) down-regulation, after exposure to 25 hydroxycholesterol. Furthermore the proteolytic degradation of125I-LDL by RPMs was inhibited by chloroquine which interferes with the lysosomal degradation processes. These findings show LDL receptor cell biology of RPM to be of the classical type and to differ from that of platelets.

d-dimensional orthogonal polynomials: Commutator theorem and other results

2017 ◽  
Vol 20 (02) ◽  
pp. 1750011
Author(s):  
Luigi Accardi ◽  
Abdallah Dhahri
Keyword(s):  
Orthogonal Polynomials ◽  
Random Variable ◽  
Product Measure ◽  
Classical Formula ◽  
Variable Formula ◽  
Commutator Theorem ◽  
The Creation ◽  
New Formulation ◽  
Preservation Operator

We give new and simplified proofs of three basic theorems in the theory of orthogonal polynomials associated to a classical, [Formula: see text]-valued random variable [Formula: see text] with all moments, namely: (1) The characterization of [Formula: see text] in terms of commutators among the creation–annihilation–preservation (CAP) operators in its quantum decomposition. (2) The characterization, in terms of the same objects, of the fact that the distribution of [Formula: see text] is a product measure. (3) The equivalence of the symmetry of [Formula: see text] with the vanishing of the associated preservation operator. Our new formulation of these results allows one to obtain a stronger form of the above statements.

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