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Function Theory and $\ell^p$ Spaces
 
Raymond Cheng Old Dominion University, Norfolk, VA
Javad Mashreghi Laval University, Quebec City, QC, Canada
William T. Ross University of Richmond, Richmond, VA
Function Theory and l^p Spaces
Softcover ISBN:  978-1-4704-5593-4
Product Code:  ULECT/75
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
eBook ISBN:  978-1-4704-6009-9
Product Code:  ULECT/75.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-1-4704-5593-4
eBook: ISBN:  978-1-4704-6009-9
Product Code:  ULECT/75.B
List Price: $110.00 $82.50
MAA Member Price: $99.00 $74.25
AMS Member Price: $88.00 $66.00
Function Theory and l^p Spaces
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Function Theory and $\ell^p$ Spaces
Raymond Cheng Old Dominion University, Norfolk, VA
Javad Mashreghi Laval University, Quebec City, QC, Canada
William T. Ross University of Richmond, Richmond, VA
Softcover ISBN:  978-1-4704-5593-4
Product Code:  ULECT/75
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
eBook ISBN:  978-1-4704-6009-9
Product Code:  ULECT/75.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-1-4704-5593-4
eBook ISBN:  978-1-4704-6009-9
Product Code:  ULECT/75.B
List Price: $110.00 $82.50
MAA Member Price: $99.00 $74.25
AMS Member Price: $88.00 $66.00
  • Book Details
     
     
    University Lecture Series
    Volume: 752020; 219 pp
    MSC: Primary 46; 30

    The classical \(\ell^{p}\) sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces \(\ell^{p}_{A}\) of analytic functions whose Taylor coefficients belong to \(\ell^p\). Relations between the Banach space \(\ell^p\) and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of \(\ell^{p}_{A}\) and a discussion of the Wiener algebra \(\ell^{1}_{A}\).

    Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

    Readership

    Graduate students and researchers interested in the connections between functional analysis and analytic function theory.

  • Table of Contents
     
     
    • Chapters
    • The basics of $\ell ^p$
    • Frames
    • The geometry of $\ell ^p$
    • Weak parallelogram laws
    • Hardy and Bergman spaces
    • $\ell ^p$ as a function space
    • Some operators on $\ell ^p_A$
    • Extremal functions
    • Zeros of $\ell ^p_A$ functions
    • The shift
    • The backward shift
    • Multipliers of $\ell ^p_A$
    • The Wiener algebra
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 752020; 219 pp
MSC: Primary 46; 30

The classical \(\ell^{p}\) sequence spaces have been a mainstay in Banach spaces. This book reviews some of the foundational results in this area (the basic inequalities, duality, convexity, geometry) as well as connects them to the function theory (boundary growth conditions, zero sets, extremal functions, multipliers, operator theory) of the associated spaces \(\ell^{p}_{A}\) of analytic functions whose Taylor coefficients belong to \(\ell^p\). Relations between the Banach space \(\ell^p\) and its associated function space are uncovered using tools from Banach space geometry, including Birkhoff-James orthogonality and the resulting Pythagorean inequalities. The authors survey the literature on all of this material, including a discussion of the multipliers of \(\ell^{p}_{A}\) and a discussion of the Wiener algebra \(\ell^{1}_{A}\).

Except for some basic measure theory, functional analysis, and complex analysis, which the reader is expected to know, the material in this book is self-contained and detailed proofs of nearly all the results are given. Each chapter concludes with some end notes that give proper references, historical background, and avenues for further exploration.

Readership

Graduate students and researchers interested in the connections between functional analysis and analytic function theory.

  • Chapters
  • The basics of $\ell ^p$
  • Frames
  • The geometry of $\ell ^p$
  • Weak parallelogram laws
  • Hardy and Bergman spaces
  • $\ell ^p$ as a function space
  • Some operators on $\ell ^p_A$
  • Extremal functions
  • Zeros of $\ell ^p_A$ functions
  • The shift
  • The backward shift
  • Multipliers of $\ell ^p_A$
  • The Wiener algebra
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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