# Search results for: Franz Peherstorfer

Journal of Approximation Theory > 2011 > 163 > 6 > 707-723

Journal of Approximation Theory > 2011 > 163 > 6 > 724-737

Journal of Approximation Theory > 2009 > 160 > 1-2 > 171-186

Constructive Approximation > 2007 > 25 > 1 > 29-39

_{2}-minimal polynomials is highly developed, so far not much is known about L

_{p}-minimal polynomials, $p\in (1,\infty) \backslash \{2\}.$ Indeed, Bernstein gave asymptotics for the minimum deviation, Fekete and Walsh gave nth root asymptotics and, recently, Lubinsky and Saff came up with asymptotics outside the support [-1,1]. But the main point of interest, the...

Computational Methods and Function Theory > 2004 > 4 > 2 > 355-390

Constructive Approximation > 2003 > 20 > 3 > 377-397

Numerische Mathematik > 2003 > 95 > 4 > 689-706

Journal of Computational and Applied Mathematics > 2003 > 153 > 1-2 > 371-385

_{n}) of orthogonal polynomials the orthogonality behaviour of the sequence of polynomials (ρ(pn∘T))n∈N is investigated. In particular necessary and sufficient conditions are given such...

Journal of Approximation Theory > 2001 > 111 > 2 > 180-195

_{l}=∪

^{l}

_{j=1}[a

_{2j−1}, a

_{2j}] and given ε>0 there exists a real polynomial T and a set of l disjoint intervals E

_{l}=∪

^{l}

_{j=1}[ã

_{2j−1}, ã

_{2j}] with E

_{l}⊇E

_{l}and ‖(ã

_{1}, …, ã

_{2l})−(a

_{1}, …, a

_{2l})‖

_{max}...

Journal of Computational and Applied Mathematics > 2001 > 133 > 1-2 > 519-534

Journal of Computational and Applied Mathematics > 2001 > 127 > 1-2 > 297-315

_{n}on K with respect to the L

_{q}(μ)-norm, q [1,~), then zero is also a best approximation to f T on T

^{-}

^{1}(K) with respect to the L

_{q}(μ

^{T})-norm, where μ

^{T}arises from μ by the transformation T. In particular, μ ...

Computational Methods and Function Theory > 2001 > 1 > 1 > 61-79

Journal of Approximation Theory > 2000 > 105 > 1 > 102-128

Journal of Approximation Theory > 2000 > 102 > 1 > 96-119

Journal of Approximation Theory > 1997 > 88 > 3 > 316-353

_{n}}n∈N

_{0}witha

_{n}∈C,a

_{n+N}=a

_{n}and |a

_{n}|<1 for alln∈N

_{0}, be a periodic sequence of reflection coefficients and let {P

_{n}}n∈N

_{0}be the associated sequence of orthogonal polynomials generated byP

_{n+1}=zP

_{n}−ā

_{n}P*

_{n}. Furthermore let {b

_{n}}n∈N

_{0}be an asymptotically periodic...

Advances in Computational Mathematics > 1997 > 7 > 3 > 401-428

*σ*and d

*µ*, respectively. In this paper we consider the question how the orthogonality measures d

*σ*and d

*µ*are related to each other if the orthogonal polynomials are connected by a relation of the form $$\sum\nolimits_{j = 0}^{k(n)} {\gamma _{j,n} {\mathcal{P}}_{n - j} (z)}...

Journal of Approximation Theory > 1996 > 87 > 1 > 60-102

_{l}=∪

^{l}

_{j=1}[ϕ

_{2j−1},

_{2j}],

_{1}<…<

_{2l}and

_{2l}−ϕ

_{1}⩽2π, such that onE

_{l}there exists a real trigonometric polynomialτ

_{N}(ϕ) with maximal number, i.e.,N+l, of extremal points onE

_{l}. The associated algebraic polynomialT

_{N}(z)=z...

Journal of Approximation Theory > 1996 > 85 > 2 > 140-184

_{l}=∪

^{l}

_{j=1}[ϕ

_{2j−1}, ϕ

_{2j}]⊆[0, 2π], R(ϕ)=∏

^{2l}

_{j=1}sin((ϕ−ϕ

_{j})/2) and[formula]forϕ∈(ϕ

_{2j−1}, ϕ

_{2j}). Furthermore let V, W be arbitrary real trigonometric polynomials such that R=VW and let A(ϕ) be a real trigonometric polynomial which has no zero inE

_{l}. First we derive an explicit representation of the Caratheodory...

Journal of Computational and Applied Mathematics > 1995 > 65 > 1-3 > 319-338