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JAT
2007
67views more  JAT 2007»
13 years 10 months ago
Rakhmanov's theorem for orthogonal matrix polynomials on the unit circle
Rakhmanov’s theorem for orthogonal polynomials on the unit circle gives a sufficient condition on the orthogonality measure for orthogonal polynomials on the unit circle, in orde...
Walter Van Assche
JAT
2007
103views more  JAT 2007»
13 years 10 months ago
Monotonicity of zeros of Jacobi polynomials
Denote by xn,k(α, β), k = 1, . . . , n, the zeros of the Jacobi polynomial P (α,β) n (x). It is well known that xn,k(α, β) are increasing functions of β and decreasing func...
Dimitar K. Dimitrov, Fernando R. Rafaeli
JAT
2007
86views more  JAT 2007»
13 years 10 months ago
Gaussian averages of interpolated bodies and applications to approximate reconstruction
We prove sharp bounds for the expectation of the supremum of the Gaussian process indexed by the intersection of Bn p with ρBn q for 1 ≤ p, q ≤ ∞ and ρ > 0, and by the ...
Y. Gordon, A. E. Litvak, Shahar Mendelson, A. Pajo...
JAT
2007
55views more  JAT 2007»
13 years 10 months ago
Chalmers-Metcalf operator and uniqueness of minimal projections
We know that not all minimal projections in Lp (1 < p < ∞) are unique (see [39]). The aim of this paper is examine the connection of the Chalmers-Metcalf operator (introduc...
Grzegorz Lewicki, Leslaw Skrzypek
JAT
2007
57views more  JAT 2007»
13 years 10 months ago
Measures, densities and diameters of frequency bands of scaling functions and wavelets
We investigate the measures of frequency bands of scaling functions and wavelets, and solve an open problem. Furthermore, we give conditions for which the measures of frequency ba...
Zhihua Zhang
JAT
2007
56views more  JAT 2007»
13 years 10 months ago
A pair of orthogonal frames
Hong Oh Kim, Rae Young Kim, Jae Kun Lim, Zuowei Sh...
JAT
2007
83views more  JAT 2007»
13 years 10 months ago
Characterization and perturbation of Gabor frame sequences with rational parameters
Let A ⊂ L2(R) be at most countable, and p, q ∈ N. We characterize various frame-properties for Gabor systems of the form G(1, p/q,A) = {e2 imxg(x − np/q) : m, n ∈ Z, g ∈...
Marcin Bownik, Ole Christensen
JAT
2007
55views more  JAT 2007»
13 years 10 months ago
The Homogeneous Approximation Property for wavelet frames
An irregular wavelet frame has the form W(ψ, Λ) = {a−1/2 ψ(x a − b)}(a,b)∈Λ, where ψ ∈ L2 (R) and Λ is an arbitrary sequence of points in the affine group A = R+ × ...
Christopher Heil, Gitta Kutyniok
JAT
2007
100views more  JAT 2007»
13 years 10 months ago
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves
Quantitative bounds on rates of approximation by linear combinations of Heaviside plane waves are obtained for sufficiently differentiable functions f which vanish rapidly enough...
Paul C. Kainen, Vera Kurková, Andrew Vogt