000 03622nam a22005055i 4500
001 978-3-0348-0572-8
003 DE-He213
005 20140220082836.0
007 cr nn 008mamaa
008 130130s2013 sz | s |||| 0|eng d
020 _a9783034805728
_9978-3-0348-0572-8
024 7 _a10.1007/978-3-0348-0572-8
_2doi
050 4 _aQA351
072 7 _aPBKF
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.5
_223
100 1 _aVolchkov, Valery V.
_eauthor.
245 1 0 _aOffbeat Integral Geometry on Symmetric Spaces
_h[electronic resource] /
_cby Valery V. Volchkov, Vitaly V. Volchkov.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2013.
300 _aX, 592 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Part 1. Analysis on Symmetric Spaces. 1 Preliminaries -- 2 The Euclidean case -- 3 Symmetric spaces of the non-compact type.-4 Analogies for compact two-point homogeneous Spaces -- 5 The phase space associated to the Heisenberg group.-Part 2. Offbeat Integral Geometry -- 1 Functions with zero ball means on Euclidean space -- 2 Two-radii theorems in symmetric spaces -- 3 The problem of finding a function from its ball means -- 4 Sets with the Pompeiu property -- 5 Functions with zero integrals over polytopes.-6 Ellipsoidal means -- 7 The Pompeiu property on a sphere -- 8 The Pompeiu transform on symmetric spaces and groups.-9 Pompeiu transforms on manifolds -- Bibliography -- Index -- Basic notation.
520 _aThe book demonstrates the development of integral geometry on domains of homogeneous spaces since 1990. It covers a wide range of topics, including analysis on multidimensional Euclidean domains and Riemannian symmetric spaces of arbitrary ranks as well as recent work on phase space and the Heisenberg group. The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern versions of the Pompeiu problem, and explicit reconstruction formulae in problems of integral geometry. These results are intriguing and useful in various fields of contemporary mathematics. The proofs given are “minimal” in the sense that they involve only those concepts and facts which are indispensable for the essence of the subject. Each chapter provides a historical perspective on the results presented and includes many interesting open problems. Readers will find this book relevant to harmonic analysis on homogeneous spaces, invariant spaces theory, integral transforms on symmetric spaces and the Heisenberg group, integral equations, special functions, and transmutation operators theory.
650 0 _aMathematics.
650 0 _aHarmonic analysis.
650 0 _aIntegral Transforms.
650 0 _aFunctions, special.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematics.
650 2 4 _aSpecial Functions.
650 2 4 _aAbstract Harmonic Analysis.
650 2 4 _aIntegral Transforms, Operational Calculus.
650 2 4 _aDifferential Geometry.
700 1 _aVolchkov, Vitaly V.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034805711
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0572-8
912 _aZDB-2-SMA
999 _c96308
_d96308