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Linear Transformations in Hilbert Space and Their Applications to Analysis
M. H. Stone

Colloquium Publications
1932; 622 pp; softcover
Volume: 15
Reprint/Revision History:
twelfth printing 2000
ISBN-10: 0-8218-1015-4
ISBN-13: 978-0-8218-1015-6
List Price: US$93.45
Member Price: US$74.76
Order Code: COLL/15
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"This book [a 1990 reprint of the 1932 original] is a classic by now."

-- Mathematical Reviews

"The author has set himself the task of giving a thorough and systematic exposition of the main features of the theory, based on his own investigations, but also containing the principal results of Carleman and von Neumann.

"Professor Stone has done us a real service by providing a clear, systematic, and readable account of this important theory which is still in statu nascendi. The book is not always easy reading, but the author is fair to the reader: nothing essential is withheld, the terminology is clearly defined and strictly adhered to, there are enough facts provided for the imagination to feed on, but no loose statements."

-- Bulletin of the AMS

Table of Contents

  • Abstract Hilbert space and its realizations
  • Transformations in Hilbert space
  • Examples of linear transformations
  • Resolvents, spectra, reducibility
  • Self-adjoint transformations
  • The operational calculus
  • The unitary equivalence of self-adjoint transformations
  • General types of linear transformations
  • Applications
  • Index
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