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Unitary Correlations and the Fejér Kernel
 Mathematical Physics, Analysis, and Geometry
, 2002
"... Let M be a unitary matrix with eigenvalues t j , and let f be a function on the unit circle. Define X f (M) = P f(t j ). We derive exact and asymptotic formulae for the covariance of X f and X g with respect to the measures j(M)j 2 dM where dM is Haar measure and an irreducible character. The ..."
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Cited by 4 (1 self)
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. The asymptotic results include an analysis of the Fej'er kernel which may be of independent interest.
Circulant Preconditioners Constructed from Kernels
 SIAM J. Numer. Anal
, 1991
"... We consider circulant preconditioners for Hermitian Toeplitz systems from the view point of function theory. We show that some wellknown circulant preconditioners can be derived from convoluting the generating function f of the Toeplitz matrix with famous kernels like the Dirichlet and the Fej& ..."
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Cited by 9 (5 self)
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We consider circulant preconditioners for Hermitian Toeplitz systems from the view point of function theory. We show that some wellknown circulant preconditioners can be derived from convoluting the generating function f of the Toeplitz matrix with famous kernels like the Dirichlet and the Fej
Summation Kernels for Orthogonal Polynomial Systems
"... The convergence of weighted Fourier expansions with respect to orthogonal polynomial systems fPn : n 2 N 0 g is studied in certain Banach spaces B ` L 1 (), where the support of the orthogonality measure is assumed to be infinite and compact. We focus on orthogonal polynomial systems which ind ..."
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induce a hypergroup structure on N 0 and a convolution structure on supp . Especially the Dirichlet kernel, a Fej'ertype kernel and the de la Vall'eePoussin kernel are studied, where we stress the analogy to the trigonometric case. Key Words. Discrete hypergroups, polynomial hypergroups
BerryEsséenType Inequalities for Ultraspherical Expansions
 Publ. Math. Debrecen
, 1999
"... This paper contains several variants of BerryEss'eentype inequalities for ultraspherical expansions of probability measures on [0; ] . Similar to the classical results on IR , proofs will be based in some cases on ultraspherical analogues of Fej'erkernels. The inequalities in this paper ..."
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Cited by 2 (1 self)
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This paper contains several variants of BerryEss'eentype inequalities for ultraspherical expansions of probability measures on [0; ] . Similar to the classical results on IR , proofs will be based in some cases on ultraspherical analogues of Fej'erkernels. The inequalities