Sigurdur Helgason

Integral Geometry and Radon Transforms

• Broschiertes Buch

Produktbeschreibung

In this text, integral geometry deals with Radon's problem of representing a function on a manifold in terms of its integrals over certain submanifolds-hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: "Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area." -Boris Rubin, Louisiana State University

Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4899-9420-2
• 2011
• Seitenzahl: 316
• Erscheinungstermin: 11. Oktober 2014
• Englisch
• Abmessung: 235mm x 155mm x 18mm
• Gewicht: 486g
• ISBN-13: 9781489994202
• ISBN-10: 1489994203
• Artikelnr.: 40703891

Autorenporträt

Dr. Sigurdur Helgason has authored or co-authered 9 books and 94 papers. He has received numerous honors and awards, including the Steele Prize, awarded by the American Mathematical Society in 1988. He has been a professor at MIT since 1960.

Inhaltsangabe

The Radon Transformon Rⁿ .- A Duality in Integral Geometry.- The Radon Transform on Two-Point Homogeneous Spaces.- The X-Ray Transform on a Symmetric Space.- Orbital Integrals.- The Mean-Value Operator.- Fourier Transforms and Distribution: A Rapid Course.- Lie Transformation Groups and Differential Operators.- Bibliography.- Notational Conventions.- Index.

Rezensionen

From the reviews:

"This specialist book in the field of geometric analysis is intended for graduate students and professionals. ... The field has several applications including medical X-ray technology and tomography. The nine-chapter volume devotes a chapter to these technologies and other applications. The book is largely self-contained, and includes a chapter at the end with necessary background material ... . The volume includes a substantial bibliography, and each chapter concludes with bibliographic notes.

Summing Up: Recommended. Graduate students and above." -- D. Z. Spicer, Choice, Vol. 48 (11), August, 2011