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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Function Theory and $/ell ^p$ Spaces (Paperback)
Loot Price: R1,481
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Function Theory and $/ell ^p$ Spaces (Paperback)
Series: University Lecture Series
Expected to ship within 12 - 19 working days
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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.
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