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Lecture Notes in Mathematics

Geometry of Müntz Spaces and Related Questions

Authors: Gurariy, Vladimir I., Lusky, Wolfgang

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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)


Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $34.99
price for USA in USD (gross)
  • ISBN 978-3-540-31546-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA in USD
  • ISBN 978-3-540-28800-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Müntz Spaces and Related Questions
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1870
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-31546-9
DOI
10.1007/11551621
Softcover ISBN
978-3-540-28800-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIII, 176
Topics