Offbeat Integral Geometry on Symmetric Spaces
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- 8924 Downloads
Springer Basel, Imprint: Birkhäuser , Basel
Harmonic analysis, Integral transforms, Global differential geometry, Abstract Harmonic Analysis, Special Functions, Differential Geometry, Mathematics, Operational Calculus Integral Trans
About the Edition
The 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 The book includes many significant recent results, some of them hitherto unpublished, among which can be pointed out uniqueness theorems for various classes of functions, far-reaching generalizations of the two-radii problem, the modern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.
|Statement||by Valery V. Volchkov, Vitaly V. Volchkov|
|Contributions||Volchkov, Vitaly V., SpringerLink (Online service)|
|The Physical Object|
|Format||[electronic resource] /|
|Pagination||XII, 590 p. 1 illus. in color.|
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Buy Offbeat Integral Geometry on Symmetric Spaces on FREE SHIPPING on qualified orders Offbeat Integral Geometry on Symmetric Spaces: Volchkov, Valery V., Volchkov, Vitaly V.: : BooksCited by: The book demonstrates the development of integral geometry on domains of homogeneous spaces since 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.
Preliminaries -- 2.
Details Offbeat Integral Geometry on Symmetric Spaces FB2
The Euclidean case -- 3. Symmetric spaces of the non-compact type -- 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. Offbeat Integral Geometry Functions with zero ball means on Euclidean space Two-radii theorems in symmetric spaces The problem of finding a function from its ball means Sets with the Pompeiu property Functions with zero integrals over polytopes Ellipsoidal means The Pompeiu property on a sphere The Pompeiu.
While a related forthcoming book, "Integral Geometry and Radon Transforms" (here denoted [IGR]) deals with several examples of homoge neous spaces in duality with corresponding Radon transforms, the present work follows the direction of the first edition and concentrates on analy sis on Riemannian symmetric spaces X = G/K.
We develop. Offbeat Integral Geometry on Symmetric Spaces. Chapter. Jan ; Valery V. Volchkov. Many formulas that are useful and important, but usually left to books, are given in the text.
This is the. This generalizes the notion of reflection in a point in ordinary Euclidean geometry. The theory of symmetric spaces implies that such spaces have a transitive group of isometries and can be represented as coset spaces G/K, where G is a connected Lie group with an involutive automorphism G whose fixed point set is (essentially) K.
pact Lie groups, Grassmannians and bounded symmetric domains. Any symmetric space has its own special geometry; euclidean, elliptic and hyperbolic geometry are only the very ﬁrst examples. On the other hand, these spaces have much in common, and there exists a rich theory. The purpose of these notes is to give a brief introduction.
Offbeat Integral Geometry on Symmetric Spaces Kieti viršeliai - Valery V. Volchkov, Vitaly V. Volchkov. Atsiliepimai. Įvertinimų nėra. Įvertink ir tu.
Įvertink ir tu. Visi atsiliepimai. Formatai:(2) Ad K is compact where Gs is the set of elements left invariant by show that symmetric pairs lead to symmetric spaces.
Download Offbeat Integral Geometry on Symmetric Spaces FB2
Curvature on a Symmetric Space We show that left invariant vector elds on the isometry group G are mapped to Killing elds in the symmetric space (M;g), which generate Jacobields and therefore provide the connection to the curvature tensor.
This volume, the second of Helgason's impressive three books on Lie groups and the geometry and analysis of symmetric spaces, is an introduction to group-theoretic methods in analysis on spaces with a group action. The first chapter deals with the three two-dimensional spaces of constant curvature, requiring only elementary methods and no Lie.
Purchase Differential geometry and symmetric spaces, Volume 12 - 1st Edition. Print Book & E-Book. ISBNOffbeat integral geometry on symmetric spaces. Article. Dec ; Vit. Volchkov; The book demonstrates the development of integral geometry on domains of homogeneous spaces since It.
“Integrable systems” and “algebraic geometry” are two classical fields in Mathematics and historically they have had fruitful interactions which have enriched both Mathematics and Theoretical Physics. This volume discusses recent developments of these two fields and also the.
Geometry and Topology. This book covers the following topics: Algebraic Nahm transform for parabolic Higgs bundles on P1, Computing HF by factoring mapping classes, topology of ending lamination space, Asymptotic behaviour and the Nahm transform of doubly periodic instantons with square integrable curvature, FI-modules over Noetherian rings.
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Totally geodesic spheres in compact symmetric spaces. Math. Ann. (l), An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces. Math. Ann.
Description Offbeat Integral Geometry on Symmetric Spaces EPUB
(), (with A. Korányi) A Fatou-type theorem for harmonic functions on symmetric spaces. Bull. Amer. Math. Soc. 74 (l), In mathematics, a symmetric space is a pseudo-Riemannian manifold whose group of symmetries contains an inversion symmetry about every point.
This can be studied with the tools of Riemannian geometry, leading to consequences in the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification.
Symmetric spaces commonly occur in differential. His research involves new integral geometry methods on symmetric spaces, resulting in fundamental existence theorems for differential equations on symmetric spaces and results on the representations of their isometry groups.
He has also introduced a Fourier transform on symmetric spaces and proved the basic results for this transform. This book is intended for a one year graduate course on Lie groups and Lie algebras.
The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture.
For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character. The L2 Convolution Algebra of a Compact Space 50 Chapter 5. Compact Symmetric and Weakly Symmetric Spaces 53 The Decomposition of L2(G=K) for Weakly Symmetric Spaces 53 Diagonalization of Invariant Linear Operators on Compact Weakly Symmetric spaces 58 Abelian Groups and Spaces with Commutative Convolution Algebra 59 Appendix A.
This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries.
The second half of the book discusses the less familiar octonion algebra, concentrating 5/5(1). Sigurður Helgason (born ) is an Icelandic mathematician whose research has been devoted to the geometry and analysis on symmetric particular he has used new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces as well as some new results on the representations of their isometry groups.
§1 Compact Symmetric Spaces. Injectivity and Local Inversion. Support Theorem §2 Noncompact Symmetric Spaces.
Global Inversion and General Support Theorem §3 Maximal Tori and Minimal Spheres in Compact Symmetric Spaces Exercises and Further Results Bibliographical Notes CHAPTER V Orbital Integrals and the Wave Operator.
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area below the x axis, so that the total integral of this function is zero between the limits [-3, 3]. This illustrates one of the key concepts of odd functions: the integral of an odd function is zero if it is evaluated by limits that are symmetric across the origin. We can verify this statement by explicitly calculating the integral.
Integral geometry and tomography: proceedings of the AMS-IMS- SIAM joint summer research conference, held June, with support from the National Science Foundation / Published: () Offbeat integral geometry on symmetric spaces by: Volchkov, V.
Published: (). Offbeat Integral Geometry on Symmetric Spaces, Hardcover by Volchkov, Valery AU $ shipping: + AU $ shipping. As with the introductory book entitled "Harmonic Analysis on Symmetric Spaces - Euclidean Space, the Sphere, and the Poincaré Upper Half Plane, the style is informal with an emphasis on motivation, concrete examples.MATH Section Worksheet 2 NAME Integrals of Symmetric Functions Integrals of Symmetric Functions Suppose f and g are continuous functions on [ a;a].
(a) If f is even [f(x) = f(x)], then R a We can split this integral up into the sum of two integrals as follows, Z a a f(x) dx = Z 0 a f(x) dx+ Z a 0.Symmetric Shapes Task 70 Years 2 - 10 Summary Each student has three pieces and has to make line symmetric shapes with them.
Doesn't sound too hard does it, but it is a very different challenge to most text book examples on symmetry where the whole is given and what is asked for is the line of symmetry.
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