Result: THE AREAS OF POLYNOMIAL IMAGES AND PRE-IMAGES: The areas of polynomial images and pre-images
Title:
THE AREAS OF POLYNOMIAL IMAGES AND PRE-IMAGES: The areas of polynomial images and pre-images
Authors:
Source:
Bulletin of the London Mathematical Society. 36:786-792
Publisher Information:
Wiley, 2004.
Publication Year:
2004
Subject Terms:
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
1469-2120
0024-6093
0024-6093
DOI:
10.1112/s0024609304003509
Access URL:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3E966CE3892D74489D78EBDAF2CE01F3/S0024609304003662a.pdf/frank_smithies_19122002.pdf
https://zbmath.org/2148920
https://doi.org/10.1112/s0024609304003509
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024609304003509
http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=254628
https://www.cambridge.org/core/journals/bulletin-of-the-london-mathematical-society/article/areas-of-polynomial-images-and-preimages/EB08D3B0CD01A65BD87B42651116C1D6
https://dialnet.unirioja.es/servlet/articulo?codigo=1017234
https://academic.oup.com/blms/article/36/6/786/319435
https://research-information.bris.ac.uk/en/publications/the-areas-of-polynomial-images-and-pre-images
https://zbmath.org/2148920
https://doi.org/10.1112/s0024609304003509
https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0024609304003509
http://journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=254628
https://www.cambridge.org/core/journals/bulletin-of-the-london-mathematical-society/article/areas-of-polynomial-images-and-preimages/EB08D3B0CD01A65BD87B42651116C1D6
https://dialnet.unirioja.es/servlet/articulo?codigo=1017234
https://academic.oup.com/blms/article/36/6/786/319435
https://research-information.bris.ac.uk/en/publications/the-areas-of-polynomial-images-and-pre-images
Accession Number:
edsair.doi.dedup.....0e86db4ef5f9dcf6b705bd7d6e5c96c4
Database:
OpenAIRE
Further Information
Let \(p\) be a monic complex polynomial of degree \(n\), and let \(K\) be a measurable subset of the complex plane. Then the area of \(p(K)\), counted with multiplicity is at least \(\Pi n(\frac{\text{Area}(K)}{\Pi})^{n}\), and the area of the pre-image of \(K\) under \(p\) is at most \(\Pi^{1-\frac{1}{n}}(\text{Area}(K))^{\frac{1}{n}}\). Both bounds are proved to be sharp. Due to Pólya, the author proved the classical result of a special case of the pre-image result in which \(K\) is a disc.