TAILIEUCHUNG - Đề tài " Radon inversion on Grassmannians via G˚ardingGindikin fractional integrals "

We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and G˚ arding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection, we obtain Abel-type representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces. | Annals of Mathematics Radon inversion on Grassmannians via G arding-Gindikin fractional integrals By Eric L. Grinberg and Boris Rubin Annals of Mathematics 159 2004 783 817 Radon inversion on Grassmannians via Garding-Gindikin fractional integrals By Eric L. Grinberg and Boris Rubin Abstract We study the Radon transform Rf of functions on Stiefel and Grassmann manifolds. We establish a connection between Rf and Garding-Gindikin fractional integrals associated to the cone of positive definite matrices. By using this connection we obtain Abel-type representations and explicit inversion formulae for Rf and the corresponding dual Radon transform. We work with the space of continuous functions and also with Lp spaces. 1. Introduction Let Gn k Gn k be a pair of Grassmann manifolds of linear fc-dimensional and fc -dimensional subspaces of Rn respectively. Suppose that 1 fc k n 1. A point n Gn k Gn k is a nonoriented fc-plane fc -plane in Rn passing through the origin. The Radon transform of a sufficiently good function f n on Gn k is a function Rf on the Grassmannian Gn k . The value of Rf Ệ at the fc -plane Ệ is the integral of the fc-plane function f n over all fc-planes n which are subspaces of Ệ 1-1 Rf y f nMn Gn k n -n i dịn being the canonical normalized measure on the space of planes n in In the present paper we focus on inversion formulae for Rf leaving aside such important topics as range characterization affine Grassmannians the complex case geometrical applications and further possible generalizations. Concerning these topics the reader is addressed to fundamental papers by . Gel fand and collaborators F. Gonzalez P. Goodey . Grinberg S. Helgason T. Kakehi . Petrov . Strichartz and others. This work was supported in part by NSF grant DMS-9971828. The second author also was supported in part by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas sponsored by the Minerva Foundation Germany . 784 ERIC L. GRINBERG AND BORIS

• Thạc sĩ - Tiến sĩ - Cao học
• Radon inversion
• subjects of mathematics
• Annals of Mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center