The Selected Works of Sigurdur HelgasonAmerican Mathematical Soc., 2009 - 715 síður Sigurdur Helgason is a leading expert in harmonic analysis and integral geometry on symmetric spaces. His work has had, and continues to have, a profound influence on the field. Helgason's work is marked by an interplay of analysis, geometry, and representation theory. The articles collected here cover invariant differential operators, geometric properties of solutions to differential equations on symmetric spaces, double fibrations in integral geometry, spherical functions and spherical transforms, duality for symmetric spaces, representation theory, and the Fourier transform on G/K. The papers are supplemented by an introductory essay by Helgason. This Selecta of Sigurdur Helgason's important papers will be a valuable resource to research mathematicians and graduate students. |
Efni
metric spaces Bull Amer Math Soc 69 1963 778781 | 69 |
Duality and Radon transform for symmetric spaces Amer | 75 |
The Radon transform on Euclidean spaces compact twopoint | 147 |
homogeneous spaces and Grassmann manifolds Acta Math | 175 |
A duality in integral geometry on symmetric spaces Proc | 183 |
Totally geodesic spheres in compact symmetric spaces Math | 419 |
Medd Danske Vid Selsk 42 1989 93102 | 551 |
Some results on invariant differential operators on symmetric spaces | 571 |
Indag Math 16 2005 531551 | 681 |
The inversion of the Xray transform on a compact symmetric | 703 |
Acknowledgments | 713 |
An analogue of the PaleyWiener theorem for the Fourier transform | 715 |
Common terms and phrases
abelian Amer analog analytic automorphism Cartan coefficients compact support complex conical distributions conjugate consider constant converges COROLLARY corresponding coset space curvature decomposition defined denote the set duality eigenfunctions eigenspace element Euclidean space follows Fourier transform function f given group representations Haar measure Harish-Chandra harmonic Hence holomorphic homogeneous spaces horocycle hyperplanes integral geometry invariant differential operators inversion formula irreducible isometry isomorphism K-finite K-invariant Killing form Laplace-Beltrami operator Lemma Let f Let G Lie algebra linear Lorentz spaces manifold mapping Math Mathematics one-to-one operators on symmetric Paley-Wiener theorem polynomial Proc proof proved radial Radon transform result satisfies semisimple Lie group SIGURÐUR HELGASON sinh sphere spherical functions subalgebra subgroup of G subspace symmetric spaces t₁ tangent space tion topology totally geodesic two-point homogeneous spaces vector wave equation Weyl chamber Weyl group λεα