Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1870)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Starting point and motivation for this volume is the classical Muentz theorem which states that the space of all polynomials on the unit interval, whose exponents have too many gaps, is no longer dense in the space of all continuous functions. The resulting spaces of Muentz polynomials are largely unexplored as far as the Banach space geometry is concerned and deserve the attention that the authors arouse. They present the known theorems and prove new results concerning, for example, the isomorphic and isometric classification and the existence of bases in these spaces. Moreover they state many open problems. Although the viewpoint is that of the geometry of Banach spaces they only assume that the reader is familiar with basic functional analysis. In the first part of the book the Banach spaces notions are systematically introduced and are later on applied for Muentz spaces. They include the opening and inclination of subspaces, bases and bounded approximation properties and versions of universality.
Reviews
From the reviews:
"This book studies Müntz spaces associated with an increasing sequence of nonnegative exponents … . This is a well-organized, well-written, thoughtful, and thought-provoking book, discussing a number of tastefully selected topics. There is no doubt that research will continue, in the footsteps of the authors, on the fascinating problems related to these topics that remain open." (Tamás Erdélyi, Mathematical Reviews, Issue 2007 g)
Bibliographic Information
Book Title: Geometry of Müntz Spaces and Related Questions
Authors: Vladimir Gurariy, Wolfgang Lusky
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/11551621
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Softcover ISBN: 978-3-540-28800-8Published: 03 November 2005
eBook ISBN: 978-3-540-31546-9Published: 22 November 2005
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 176
Topics: Functional Analysis, Geometry