1,146 research outputs found
Marcinkiewicz--Zygmund measures on manifolds
Let be a compact, connected, Riemannian manifold (without
boundary), be the geodesic distance on , be a
probability measure on , and be an orthonormal system
of continuous functions, for all ,
be an nondecreasing sequence of real numbers with
, as , , . We describe conditions to ensure an
equivalence between the norms of elements of with their suitably
discretized versions. We also give intrinsic criteria to determine if any
system of weights and nodes allows such inequalities. The results are stated in
a very general form, applicable for example, when the discretization of the
integrals is based on weighted averages of the elements of on geodesic
balls rather than point evaluations.Comment: 28 pages, submitted for publicatio
Fine Structure of the Zeros of Orthogonal Polynomials, II. OPUC With Competing Exponential Decay
We present a complete theory of the asymptotics of the zeros of OPUC with
Verblunsky coefficients where and \abs{b_\ell} = b<1.Comment: Keywords: orthogonal polynomials, Jacobi matrices, CMV matrice
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