A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p&gt;2lp

Khrushchev, Sergei

doi:10.1006/jath.2000.3501

Cited by 9 publications

(6 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By Rakhmanov's theorem Nevai's class contains Erdo s' class. There are examples of pure jump measures [5,31,33], pure singular continuous measures [32], including some singular Riesz products [28], in Nevai's class. Totik [59] constructed further important examples of measures in Nevai's class.…”

Section: The Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Schur's Algorithm, Orthogonal Polynomials, and Convergence of Wall's Continued Fractions in L2(T)

Khrushchev¹

2001

Journal of Approximation Theory

Self Cite

133

View full text Add to dashboard Cite

Section: The Resultsmentioning

confidence: 99%

“…For example, it is shown in [28] that there exist infinite Blaschke products such that for }=1, 2, ..., but lim n # n >0. Then f is an inner function.…”

Section: Convergence Of Continued Fractions In Measurementioning

confidence: 97%

Schur's Algorithm, Orthogonal Polynomials, and Convergence of Wall's Continued Fractions in L2(T)

Khrushchev¹

2001

Journal of Approximation Theory

Self Cite

133

View full text Add to dashboard Cite

“…It is known (see [10,20,21,22,29,40]) that when ∞ n=1 |a n − 1| 2 + |b n | 2 = ∞, dµ can stop having an a.c. component, so we will need an additional condition. What we will use is…”

Section: Introductionmentioning

confidence: 99%

Monotone Jacobi parameters and non-Szegő weights

Kreimer

Simon

2009

Journal of Approximation Theory

View full text Add to dashboard Cite

show abstract

“…We show now that there are universal measures whose Schur functions are Blaschke products (cf. [20,Corollary 1]). …”

Section: S=1mentioning

confidence: 91%

Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures

Golinskiĭ

Khrushchev

2002

Journal of Approximation Theory

Self Cite

View full text Add to dashboard Cite

The convergence in L 2 (T) of the even approximants of the Wall continued fractions is extended to the Cesàro-Nevai class CN, which is defined as the class of probability measures s with lim n Q . 1 n ; n − 1 k=0 |a k |=0, {a n } n \ 0 being the Geronimus parameters of s. We show that CN contains universal measures, that is, probability measures for which the sequence {|j n | 2 ds} n \ 0 is dense in the set of all probability measures equipped with the weak-* topology. We also consider the ''opposite'' Szegő class which consists of measures with ;.1/2 < . and describe it in terms of Hessenberg matrices. © 2002 Elsevier Science (USA)

show abstract

A Singular Riesz Product in the Nevai Class and Inner Functions with the Schur Parameters in ∩p>2lp

Cited by 9 publications

References 6 publications

Schur's Algorithm, Orthogonal Polynomials, and Convergence of Wall's Continued Fractions in L2(T)

Schur's Algorithm, Orthogonal Polynomials, and Convergence of Wall's Continued Fractions in L2(T)

Monotone Jacobi parameters and non-Szegő weights

Cesàro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures

Contact Info

Product

Resources

About