On the spacing of zeros of paraorthogonal polynomials for singular measures

Jonathan Breuer; Eyal Seelig

doi:https://doi.org/10.1016/j.jat.2020.105482

On the spacing of zeros of paraorthogonal polynomials for singular measures

Jonathan Breuer, Eyal Seelig

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a lower bound on the spacing of zeros of paraorthogonal polynomials on the unit circle, based on continuity of the underlying measure as measured by Hausdorff dimensions. We complement this with the analog of the result from Breuer (2011) showing that clock spacing holds even for certain singular continuous measures.

Original language	English
Article number	105482
Journal	Journal of Approximation Theory
Volume	259
DOIs	https://doi.org/10.1016/j.jat.2020.105482
State	Published - Nov 2020

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Numerical Analysis
General Mathematics

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title = "On the spacing of zeros of paraorthogonal polynomials for singular measures",

abstract = "We prove a lower bound on the spacing of zeros of paraorthogonal polynomials on the unit circle, based on continuity of the underlying measure as measured by Hausdorff dimensions. We complement this with the analog of the result from Breuer (2011) showing that clock spacing holds even for certain singular continuous measures.",

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AB - We prove a lower bound on the spacing of zeros of paraorthogonal polynomials on the unit circle, based on continuity of the underlying measure as measured by Hausdorff dimensions. We complement this with the analog of the result from Breuer (2011) showing that clock spacing holds even for certain singular continuous measures.

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M3 - مقالة

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JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

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On the spacing of zeros of paraorthogonal polynomials for singular measures

Abstract

All Science Journal Classification (ASJC) codes

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