On the generalized quotient integrals on homogeneous spaces
-
Tajedin Derikvand
and
Mohammad Janfada
Abstract
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.
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. 10.1063/1.1729798Search in Google Scholar
[2] A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. II, J. Appl. Phys. 35 (1964), 2908–2912. 10.1063/1.1713127Search in Google Scholar
[3] S. R. Deans, The Radon Transform and Some of its Applications, Wiley, New York, 1983. Search in Google Scholar
[4] G. B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995. Search in Google Scholar
[5] S. Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153–180. 10.1007/BF02391776Search in Google Scholar
[6] S. Helgason, Integral Geometry and Radon Transform, Springer, New York, 2011. 10.1007/978-1-4419-6055-9Search in Google Scholar
[7] E. K. Kaniuth and K. F. Taylor, Induced representations of locally compact groups, Cambridge University Press, Cambridge, 2013. 10.1017/CBO9781139045391Search in Google Scholar
[8] D. Ludwig, The Radon transform on Euclidean space, Comm. Pure Appl. Math. 17 (1966), 49–81. 10.1002/cpa.3160190105Search in Google Scholar
[9] N. Tavalaei, On the function spaces and wavelets on homogeneous spaces, Ph.D. thesis, Ferdowsi University of Mashhad, 2008. Search in Google Scholar
[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. 10.1016/0022-247X(83)90165-8Search in Google Scholar
[11] J. Radon, On the determination of functions from their integral values along certain manifolds, IEEE Trans. Med. Imaging 5 (1986), 170–176. 10.1109/TMI.1986.4307775Search in Google Scholar PubMed
[12] R. Reiter and J. D. Stegeman, Classical Harmonic Analysis, 2nd ed., Oxford University Press, New York, 2000. 10.1093/oso/9780198511892.003.0001Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Dynamics of typical Baire-1 functions on the interval
- On the generalized quotient integrals on homogeneous spaces
- An integral expression for the Dunkl kernel in the dihedral setting
- Takagi function revisited
- On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires
- Pexider type equation on a region
- Anti-periodic solutions for a higher order difference equation with p-Laplacian
- Portfolio immunization under cone restrictions
- The Lagrange multiplier and the stationary Stokes equations
- Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument
Articles in the same Issue
- Frontmatter
- Dynamics of typical Baire-1 functions on the interval
- On the generalized quotient integrals on homogeneous spaces
- An integral expression for the Dunkl kernel in the dihedral setting
- Takagi function revisited
- On the stability of steady-states of a two-dimensional system of ferromagnetic nanowires
- Pexider type equation on a region
- Anti-periodic solutions for a higher order difference equation with p-Laplacian
- Portfolio immunization under cone restrictions
- The Lagrange multiplier and the stationary Stokes equations
- Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument
