×

On the generalized quotient integrals on homogeneous spaces. (English) Zbl 1378.43007

Summary: 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.

MSC:

43A85 Harmonic analysis on homogeneous spaces

References:

[1] A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. I, J. Appl. Phys. 34 (1963), 2722-2727.; Cormack, A. M., Representation of a function by its line integrals, with some radiological applications. I, J. Appl. Phys., 34, 2722-2727 (1963) · Zbl 0117.32303
[2] A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. II, J. Appl. Phys. 35 (1964), 2908-2912.; Cormack, A. M., Representation of a function by its line integrals, with some radiological applications. II, J. Appl. Phys., 35, 2908-2912 (1964) · Zbl 0122.18401
[3] S. R. Deans, The Radon Transform and Some of its Applications, Wiley, New York, 1983.; Deans, S. R., The Radon Transform and Some of its Applications (1983) · Zbl 0561.44001
[4] G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.; Folland, G. B., A Course in Abstract Harmonic Analysis (1995) · Zbl 0857.43001
[5] S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153-180.; Helgason, S., The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math., 113, 153-180 (1965) · Zbl 0163.16602
[6] S. Helgason, Integral Geometry and Radon Transform, Springer, New York, 2011.; Helgason, S., Integral Geometry and Radon Transform (2011) · Zbl 1210.53002
[7] E. K. Kaniuth and K. F. Taylor, Induced representations of locally compact groups, Cambridge University Press, Cambridge, 2013.; Kaniuth, E. K.; Taylor, K. F., Induced representations of locally compact groups (2013) · Zbl 1263.22005
[8] D. Ludwig, The Radon transform on Euclidean space, Comm. Pure Appl. Math. 17 (1966), 49-81.; Ludwig, D., The Radon transform on Euclidean space, Comm. Pure Appl. Math., 17, 49-81 (1966) · Zbl 0134.11305
[9] N. Tavalaei, On the function spaces and wavelets on homogeneous spaces, Ph.D. thesis, Ferdowsi University of Mashhad, 2008.; Tavalaei, N., On the function spaces and wavelets on homogeneous spaces (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.; Quinto, E. T., The invertibility of rotation invariant Radon transforms, J. Math. Anal. Appl., 91, 510-521 (1983) · Zbl 0517.44009
[11] J. Radon, On the determination of functions from their integral values along certain manifolds, IEEE Trans. Med. Imaging 5 (1986), 170-176.; Radon, J., On the determination of functions from their integral values along certain manifolds, IEEE Trans. Med. Imaging, 5, 170-176 (1986)
[12] R. Reiter and J. D. Stegeman, Classical Harmonic Analysis, 2nd ed., Oxford University Press, New York, 2000.; Reiter, R.; Stegeman, J. D., Classical Harmonic Analysis (2000) · Zbl 0965.43001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.