Frontiers in Mathematics

The Hardy Space of a Slit Domain

Authors: Aleman, Alexandru, Feldman, Nathan S., Ross, William T.

  • Only book which covers Hardy spaces of slit domains

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eBook $54.99
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  • ISBN 978-3-0346-0098-9
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Softcover $69.99
price for USA
  • ISBN 978-3-0346-0097-2
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About this book

If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .

Reviews

From the reviews:

“This memoir is concerned with the description of the shift-invariant subspaces of a Hardy space on a slit domain … . this brief monograph represents an interesting and valuable contribution to the literature on the subject of shift-invariant subspaces. It should be helpful for researchers and advanced graduate students specializing in the field.” (Dragan Vukotić, Mathematical Reviews, Issue 2011 m)

Table of contents (11 chapters)

  • Introduction

    Aleman, Alexandru (et al.)

    Pages 1-7

  • Preliminaries

    Aleman, Alexandru (et al.)

    Pages 9-23

  • Nearly invariant subspaces

    Aleman, Alexandru (et al.)

    Pages 25-46

  • Nearly invariant and the backward shift

    Aleman, Alexandru (et al.)

    Pages 47-57

  • Nearly invariant and de Branges spaces

    Aleman, Alexandru (et al.)

    Pages 59-63

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0346-0098-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-0346-0097-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Hardy Space of a Slit Domain
Authors
Series Title
Frontiers in Mathematics
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-0346-0098-9
DOI
10.1007/978-3-0346-0098-9
Softcover ISBN
978-3-0346-0097-2
Series ISSN
1660-8046
Edition Number
1
Number of Pages
144
Topics