Two universality results for polynomial reproducing kernels
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We prove two new universality results for polynomial reproducing kernels of compactly supported measures. The first applies to measures on the unit circle with a jump and a singularity in the weight at $1$ and the second applies to area-type measures on a certain disconnected polynomial lemniscate. In both cases, we apply methods developed by Lubinsky to obtain our results.
21 pages, 1 figure. Version 2 incorporates new references that shorten and simplify the proofs in Section 2. Other minor typos are corrected
- Baylor University United States
reproducing kernels, Mathematics - Classical Analysis and ODEs, Christoffel functions, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, universality, confluent hypergeometric functions, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials
reproducing kernels, Mathematics - Classical Analysis and ODEs, Christoffel functions, Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\), Classical Analysis and ODEs (math.CA), FOS: Mathematics, universality, confluent hypergeometric functions, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials
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