We study the asymptotic behavior of <mml:math alttext="$L_{p}(\sigma)$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>σ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> extremal polynomials with respect to a measure of the form <mml:math alttext="$\sigma =\alpha +\gamma$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi><mml:mo>=</mml:mo><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:math>, where <mml:math alttext="$\alpha$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> is a measure concentrated on a rectifiable Jordan curve in the complex plane and <mml:math alttext="$\gamma$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi></mml:math> is a discrete measure concentrated on an infinite number of mass points.

Strong asymptotics for <mml:math alttext="$L_{p}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msub></mml:math> extremal polynomials off a complex curve

Strong asymptotics for <svg style="vertical-align:-5.73167pt" height="18.3125" version="1.1" viewBox="0 0 17.512501 18.3125" width="17.512501" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.113)"><path id="x1D43F" d="M559 163q-23 -66 -68 -163h-474l6 26q62 4 79.5 19.5t28.5 75.5l78 409q7 35 8.5 49t-8 25t-24 13t-51.5 5l5 28h266l-6 -28q-65 -5 -79.5 -18t-25.5 -74l-76 -406q-10 -57 14 -75q12 -13 96 -13q93 0 126 29q41 40 76 109z" /></g><g transform="matrix(.012,-0,0,-.012,9.763,15.188)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g></svg> extremal polynomials off a complex curve

Journal of Applied Mathematics

Strong asymptotics for Lp extremal polynomials off a complex curve

Abstract

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