Weakly convergent sequences of functions and orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomials and analytic functions
For a positive definite infinite matrix A, we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation An of size n×n. For the particular case of A being a Hankel or a Hankel block matrix, our results lead to a characterization of positive measures with finite index of determinacy and of completel...
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The relation between small oscillations of one-dimensional mechanical «-particle systems and the theory of orthogonal polynomials is investigated. It is shown how the polynomials provide a natural tool to determine the eigenfrequencies and eigencoordinates completely, where the existence of a specific two-termed recurrence formula is essential. Physical and mathematical statements are formulate...
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Riordan group concepts are combined with the basic properties of convolution families of polynomials and Sheffer sequences, to establish a duality law, canonical forms ρ(n,m) = ( n m ) cFn−m(m), c 6= 0, and extensions ρ(x, x − k) = (−1) xcFk(x), where the Fk(x) are polynomials in x, holding for each ρ(n,m) in a Riordan array. Examples ρ(n,m) = ( n m ) Sk(x) are given, in which the Sk(x) are “or...
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The rational Cherednik algebra H is a certain algebra of differential-reflection operators attached to a complex reflection group W and depending on a set of central parameters. Each irreducible representation S of W corresponds to a standard module M(λ) for H. This paper deals with the infinite family G(r, 1, n) of complex reflection groups; our goal is to study the standard modules using a co...
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A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials { 2Φ1(q−n, qb+1; q−c+b−n; q, qz)}n=0, where 0 < q < 1 and the complex parameters b, c and d are such that b = −1,−2, . . ., c− b+ 1 = −1,−2, . ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1991
ISSN: 0021-9045
DOI: 10.1016/0021-9045(91)90095-r