On the generalized quotient integrals on homogeneous spaces

• Autorzy: Derikvand T. , Kamyabi-Gol R. A. , Janfada M.

Identyfikatory

DOI

10.1515/jaa-2017-0010

• Języki publikacji: EN

Abstrakty

EN

A generalization of the quotient integral formula is presented and some of its properties are investigated. Also the relations between two function spaces related to the special homogeneous spaces are derived by using the general quotient integral formula. Finally, our results are supported by some examples.

Słowa kluczowe

EN

Radon transform; homogeneous space; strongly quasi-invariant measure

PL

transformata Radona; przestrzenie jednorodne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2017
• Tom: Vol. 23, nr 2
• Strony: 65--71
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Derikvand T.

• International Campus, Faculty of Mathematic Sciences, Ferdowsi University of Mashhad, Mashhad, Iran

autor

Kamyabi-Gol R. A.

• Department of Pure Mathematics and Centre of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran

autor

Janfada M.

• Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad, Iran

Bibliografia

• [1] A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. I, J. Appl. Phys. 34 (1963), 2722-2727.
• [2] A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. II, J. Appl. Phys. 35 (1964), 2908-2912.
• [3] S. R. Deans, The Radon Transform and Some of its Applications, Wiley, New York, 1983.
• [4] G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.
• [5] S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153-180.
• [6] S. Helgason, Integral Geometry and Radon Transform, Springer, New York, 2011.
• [7] E. K. Kaniuth and K. F. Taylor, Induced representations of locally compact groups, Cambridge University Press, Cambridge, 2013.
• [8] D. Ludwig, The Radon transform on Euclidean space, Comm. Pure Appl. Math. 17 (1966), 49-81.
• [9] N. Tavalaei, On the function spaces and wavelets on homogeneous spaces, Ph.D. thesis, Ferdowsi University of Mashhad, 2008.
• [10] E. T. Quinto, The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl. 91 (1983), 510-521; erratum, J. Math. Anal. Appl. 94 (1983), 602-603.
• [11] J. Radon, On the determination of functions from their integral values along certain manifolds, IEEE Trans. Med. Imaging 5 (1986), 170-176.
• [12] R. Reiter and J. D. Stegeman, Classical Harmonic Analysis, 2nd ed., Oxford University Press, New York, 2000.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).