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1
Content available remote

On the continued fractions of quadratic surds

100%
Cantor D.
Acta Arithmetica
|
1994
|
tom 68
|
nr 4
295-305
2
Content available remote

'The mother of all continued fractions'

100%
Dajani K., Kraaikamp C.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 1
109-123
EN
We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known as the full continued fraction), and obtain the ergodic system underlying the Farey expansion.
3
Content available remote

Relations between the orthogonal matrix polynomials on [a, b], Dyukarev-Stieltjes parameters, and Schur complements

100%
Choque-Rivero A. E.
Special Matrices
|
2017
|
tom 5
|
nr 1
303-318
EN
We obtain explicit interrelations between new Dyukarev-Stieltjes matrix parameters and orthogonal matrix polynomials on a finite interval [a, b], as well as the Schur complements of the block Hankel matrices constructed through the moments of the truncated Hausdorff matrix moment (THMM) problem in the nondegenerate case. Extremal solutions of the THMM problem are described with the help of matrix continued fractions.
4
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Limit points of eigenvalues of truncated unbounded tridiagonal operators

88%
Ifantis E. K., Kokologiannaki C. G., Petropoulou E.
Open Mathematics
|
2007
|
tom 5
|
nr 2
335-344
EN
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
5
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Continued fractions of Laurent series with partial quotients from a given set

88%
Lauder A.
Acta Arithmetica
|
1999
|
tom 90
|
nr 3
251-271
6
Content available remote

On block recursions, Askey's sieved Jacobi polynomials and two related systems

75%
Aldana B. H., Charris J. A., Mora-Valbuena O.
Colloquium Mathematicum
|
1998
|
tom 78
|
nr 1
57-91
EN
Two systems of sieved Jacobi polynomials introduced by R. Askey are considered. Their orthogonality measures are determined via the theory of blocks of recurrence relations, circumventing any resort to properties of the Askey-Wilson polynomials. The connection with polynomial mappings is examined. Some naturally related systems are also dealt with and a simple procedure to compute their orthogonality measures is devised which seems to be applicable in many other instances.
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