Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(3): 821-831

Printed May 31, 2016

https://doi.org/10.4134/BKMS.b150355

Copyright © The Korean Mathematical Society.

Hermitian algebra on generalized lemniscates

Mihai Putinar

Newcastle University

Abstract

A case study is added to our recent work on Quillen phenomenon.Pointwise positivity of polynomials on generalized lemniscates of the complex plane is related to sums of hermitian squares of rational functions, and via operator quantization, to essential subnormality.

Keywords: generalized lemniscate, positive polynomial, hermitian square, quadrature domain, subnormal operator

MSC numbers: 11E25, 47B20, 30C20

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