000			03123nam a22004815i 4500
001			978-1-4419-6055-9
003			DE-He213
005			20140220083720.0
007			cr nn 008mamaa
008			101029s2011 xxu| s |||| 0|eng d
020			_a9781441960559 _9978-1-4419-6055-9
024	7		_a10.1007/978-1-4419-6055-9 _2doi
050		4	_aQA641-670
072		7	_aPBMP _2bicssc
072		7	_aMAT012030 _2bisacsh
082	0	4	_a516.36 _223
100	1		_aHelgason, Sigurdur. _eauthor.
245	1	0	_aIntegral Geometry and Radon Transforms _h[electronic resource] / _cby Sigurdur Helgason.
264		1	_aNew York, NY : _bSpringer New York, _c2011.
300			_aXIII, 301p. 28 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aThe 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.
520			_aIn 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 differential 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 fibration, 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
650		0	_aMathematics.
650		0	_aTopological Groups.
650		0	_aGlobal analysis.
650		0	_aIntegral Transforms.
650		0	_aGlobal differential geometry.
650	1	4	_aMathematics.
650	2	4	_aDifferential Geometry.
650	2	4	_aIntegral Transforms, Operational Calculus.
650	2	4	_aGlobal Analysis and Analysis on Manifolds.
650	2	4	_aTopological Groups, Lie Groups.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781441960542
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4419-6055-9
912			_aZDB-2-SMA
999			_c105576 _d105576