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The Radon Transform(1999th Edition)

Authors:

Sigurdur Helgason

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Book details

ISBN: 1475714653, 978-1475714654

Book publisher: Springer

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Book Summary: The First Edition Of This Book Has Been Out Of Print For Some Time And I Have Decided To Follow The Publisher's Kind Suggestion To Prepare A New Edition. Many Examples With Explicit Inversion Formulas And Range Theo Rems Have Been Added, And The Group-theoretic Viewpoint Emphasized. For Example, The Integral Geometric Viewpoint Of The Poisson Integral For The Disk Leads To Interesting Analogies With The X-ray Transform In Euclidean 3-space. To Preserve The Introductory Flavor Of The Book The Short And Self-contained Chapter Von Schwartz' Distributions Has Been Added. Here §5 Provides Proofs Of The Needed Results About The Riesz Potentials While §§3-4 Develop The Tools From Fourier Analysis Following Closely The Account In Hormander's Books (1963] And [1983]. There Is Some Overlap With My Books (1984] And [1994b] Which However Rely Heavily On Lie Group Theory. The Present Book Is Much More Elementary. I Am Indebted To Sine Jensen For A Critical Reading Of Parts Of The Manuscript And To Hilgert And Schlichtkrull For Concrete Contributions Men Tioned At Specific Places In The Text. Finally I Thank Jan Wetzel And Bonnie Friedman For Their Patient And Skillful Preparation Of The Manuscript.