A generalized Fourier transform and convolution on time scales

Journal of Mathematical Analysis and Applications

Volumn 340, Issue 2, 2008, Pages 901-919

  Marks II, Robert J ^a   Gravagne, Ian A ^a   Davis, John M ^b  

^a Baylor University   (United States)

^b BAYLOR UNIVERSITY   (United States)

Author keywords

Convolution; Fourier analysis; Generalized Fourier transform; Hilger circle; Time scale

Indexed keywords

EID: 38049010460     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.08.056     Document Type: Article

References (14)

1. Agarwal R., Bohner M., O'Regan D., and Peterson A. Dynamic equations on time scales: A survey. J. Comput. Appl. Math. 141 (2002) 1-26
2. Bohner M., and Peterson A. Advances in Dynamic Equations on Time Scales (2003), Birkhäuser
3. Bohner M., and Peterson A. Dynamic Equations on Time Scales: An Introduction with Applications (2001), Birkhäuser
4. Davis J.M., Gravagne I.A., Jackson B.J., Marks II R.J., and Ramos A.A. The Laplace transform on time scales revisited. J. Math. Anal. Appl. 332 (2007) 1291-1307
5. Haralick R.M. Mathematical Morphology: Theory and Hardware (2005), Oxford University Press
6. Haralick R.M., and Shapiro L.G. Computer and Robot Vision (1991), Addison-Wesley
7. Hilger S. Analysis on measure chains-A unified approach to continuous and discrete calculus. Results Math. 18 (1990) 18-56
8. Hilger S. An application of calculus on measure chains to Fourier theory and Heisenberg's uncertainty principle. J. Difference Equ. Appl. 8 (2002) 897-936
9. S. Hilger, Ein Masskettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universität Würzburg, 1988
10. Hilger S. Special functions, Laplace and Fourier transform on measure chains. Dynam. Systems Appl. 8 (1999) 471-488
11. Marks II R.J. Introduction to Shannon Sampling and Interpolation Theory (1991), Springer-Verlag
12. Marks II R.J., and Larson J.N. One-dimensional Mellin transformation using a single optical element. Appl. Optics 18 (1979) 754-755
13. Papoulis A., and Pillai S.U. Probability, Random Variables and Stochastic Processes. fourth ed. (2001), McGraw-Hill Science
14. Soderstrand M.A. Residue Number System Arithmetic: Modern Applications in Digital Signal Processing (1986), IEEE Press